Theorem pm2.43 63

Description: Absorption of redundant antecedent. Also called the "Contraction" or "Hilbert" axiom. Theorem *2.43 of [WhiteheadRussell] p. 106. (The proof was shortened by 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 62	. 2 |- (ph -> ((ph -> ps) -> ps))
2	1	a2i 9	1 |- ((ph -> (ph -> ps)) -> (ph -> ps))

Syntax hints:   -> wi 3

This theorem is referenced by:  pm2.43i 64  pm5.4 167  rgen2a 1702  trel 2692  ssrel 3253  tfrlem1 3917  suplem1pr 5173  pre-axsup 5303

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-mp 7

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