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Axiom ax-2 7
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; see Proposition 2 of [Frege1879] p. 26. 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 pm5.41 355. (Contributed by NM, 5-Aug-1993.)
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  13  id1  22  a2d  25  dfbi1gb  187  imdi  354  sbi1  2142  ralim  2831  difin0ss  3780  sbi1NEW11  31115
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