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Axiom ax-2 6
Description: Axiom Frege. Axiom A2 of [Margaris] p. 49. This axiom "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 pm5.41 238. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
ax-2 ((φ → (ψχ)) → ((φψ) → (φχ)))

Detailed syntax breakdown of Axiom ax-2
StepHypRef Expression
1 wph . . 3 wff φ
2 wps . . . 4 wff ψ
3 wch . . . 4 wff χ
42, 3wi 4 . . 3 wff (ψχ)
51, 4wi 4 . 2 wff (φ → (ψχ))
61, 2wi 4 . . 3 wff (φψ)
71, 3wi 4 . . 3 wff (φχ)
86, 7wi 4 . 2 wff ((φψ) → (φχ))
95, 8wi 4 1 wff ((φ → (ψχ)) → ((φψ) → (φχ)))
Colors of variables: wff set class
This axiom is referenced by:  a2i  10  id1  18  a2d  21  imdi  237  sbi1v  1691  ralim  2249
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