Theorem pm2.43 47

Description: Absorption of redundant antecedent. Also called the "Contraction" or "Hilbert" axiom. Theorem *2.43 of [WhiteheadRussell] p. 106. (Contributed by NM, 5-Aug-1993.) (Proof shortened by O'Cat, 15-Aug-2004.)

Assertion

Ref	Expression
pm2.43	⊢ ((φ → (φ → ψ)) → (φ → ψ))

Proof of Theorem pm2.43

Step	Hyp	Ref	Expression
1		pm2.27 35	. 2 ⊢ (φ → ((φ → ψ) → ψ))
2	1	a2i 12	1 ⊢ ((φ → (φ → ψ)) → (φ → ψ))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  pm5.4  351