Theorem pm2.43 56

Description: Absorption of redundant antecedent. Also called the "Contraction" or "Hilbert" axiom. Theorem *2.43 of [WhiteheadRussell] p. 106. (Contributed by NM, 10-Jan-1993.) (Proof shortened by Mel L. O'Cat, 15-Aug-2004.)

Assertion

Ref	Expression
pm2.43	|- ( ( ph -> ( ph -> ps ) ) -> ( ph -> ps ) )

Proof of Theorem pm2.43

Step	Hyp	Ref	Expression
1		pm2.27 42	. 2 |- ( ph -> ( ( ph -> ps ) -> ps ) )
2	1	a2i 14	1 |- ( ( ph -> ( ph -> ps ) ) -> ( ph -> ps ) )

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  377  ax13b  1964  ralbidar  38649  rexbidar  38650