text: # Modus Ponendo Ponens
  
  ## Proof Rule
  
  Modus Ponendo Ponens is a valid argument in types of logic dealing with conditionals $\implies$.
  
  This includes propositional logic and predicate logic, and in particular natural deduction.
  
  ### Proof Rule
  
  If we can conclude $\phi \implies \psi$, and we can also conclude $\phi$, then we may infer $\psi$.
  
  ### Sequent Form
  
   $\ds p$ $\implies$ $\ds q$ $\ds p$  $\ds$ $\ds \vdash \ \$ $\ds q$  $\ds$
  
  ## Variants
  
  The following forms can be used as variants of this theorem:
  
  ### Variant 1
  
  $p \vdash \paren {p \implies q} \implies q$
  
  ### Variant 2
  
  $\vdash p \implies \paren {\paren {p \implies q} \implies q}$
  
  ### Variant 3
  
  $\vdash \paren {\paren {p \implies q} \land p} \implies q$
  
  ## Examples
  
  ### Jones is Mortal
  
  The following is an example of use of Modus Ponendo Ponens:
  
  If Jones is a man, then Jones is mortal.
  Jones is a man.
  Therefore, Jones is Mortal.
  
  ## Also known as
  
  Modus Ponendo Ponens is also known as:
  
  ## Also see
  
  The following are related argument forms:
  
  ## Linguistic Note
  
  Modus Ponendo Ponens is Latin for mode that by affirming, affirms.
  
  The shorter form Modus Ponens means mode that affirms.
explanation: The provided text is an explanation of the logical argument form known as Modus Ponendo Ponens. It includes a definition, proof rule, sequent form, variants, an example, and some linguistic notes. The text does not contain a math question or an answer to a math question.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Modus Ponendo Ponens
  
  ## Proof Rule
  
  Modus Ponendo Ponens is a valid argument in types of logic dealing with conditionals $\implies$.
  
  This includes propositional logic and predicate logic, and in particular natural deduction.
  
  ### Proof Rule
  
  If we can conclude $\phi \implies \psi$, and we can also conclude $\phi$, then we may infer $\psi$.
  
  ### Sequent Form
  
   $\ds p$ $\implies$ $\ds q$ $\ds p$  $\ds$ $\ds \vdash \ \$ $\ds q$  $\ds$
  
  ## Variants
  
  The following forms can be used as variants of this theorem:
  
  ### Variant 1
  
  $p \vdash \paren {p \implies q} \implies q$
  
  ### Variant 2
  
  $\vdash p \implies \paren {\paren {p \implies q} \implies q}$
  
  ### Variant 3
  
  $\vdash \paren {\paren {p \implies q} \land p} \implies q$
  
  ## Examples
  
  ### Jones is Mortal
  
  The following is an example of use of Modus Ponendo Ponens:
  
  If Jones is a man, then Jones is mortal.
  Jones is a man.
  Therefore, Jones is Mortal.
  
  ## Also known as
  
  Modus Ponendo Ponens is also known as:
  
  ## Also see
  
  The following are related argument forms:
  
  ## Linguistic Note
  
  Modus Ponendo Ponens is Latin for mode that by affirming, affirms.
  
  The shorter form Modus Ponens means mode that affirms.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is an explanation of the logical argument form known as Modus Ponendo Ponens. It includes a definition, proof rule, sequent form, variants, an example, and some linguistic notes. The text does not contain a math question or an answer to a math question.
  
  Label: no-question