 As Heyting emphasizes here, the theorems of Principia Mathematica also had to be looked at, for a theorem might be intuitionistically acceptable even when a classical proof given for it is  not.[26]  It is worth noting that Heyting used this method of crossing out, as also Kolmogorov had, instead of determining the logic directly from general considerations on mathematical constructions in Brouwer’s sense. (To some extent, Kreisel tried to do that systematically in the 1960s.)  In his dissertation on intuitionistic axiomatization of projective geometry, Heyting had already gained experience with developing an intuitionistic system by taking a classical axiomatic system as guideline and then adjusting  it.[27]