Theorem pm2.43 53

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 40	. 2 ⊢ (𝜑 → ((𝜑 → 𝜓) → 𝜓))
2	1	a2i 11	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  248  ralm  3519