ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ax-2 Unicode version

Axiom ax-2 6
Description: Axiom Frege. Axiom A2 of [Margaris] p. 49. One of the 3 axioms of propositional calculus. It "distributes" an antecedent over two consequents. This axiom was part of Frege's original system and is known as Frege in the literature. It is also proved as Theorem *2.77 of [WhiteheadRussell] p. 108. The other direction of this axiom also turns out to be true, as demonstrated by pm5.41 239.
Assertion
Ref Expression
ax-2

Detailed syntax breakdown of Axiom ax-2
StepHypRef Expression
1 wph . . 3
2 wps . . . 4
3 wch . . . 4
42, 3wi 4 . . 3
51, 4wi 4 . 2
61, 2wi 4 . . 3
71, 3wi 4 . . 3
86, 7wi 4 . 2
95, 8wi 4 1
Colors of variables: wff set class
This axiom is referenced by:  a2i  11  id1  19  a2d  22  imdi  238  sbi1  1668
  Copyright terms: Public domain W3C validator