Theorem pm2.43 77

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 76	. 2 |- (ph -> ((ph -> ps) -> ps))
2	1	a2i 10	1 |- ((ph -> (ph -> ps)) -> (ph -> ps))

Syntax hints:   -> wi 3

This theorem is referenced by:  pm5.4 184  rgen2aOLD 2161  trelOLD 3419  ssrelOLD 4076  ssrelrelOLD 4084  tfrlem1 5119  pm2.43bgbi 5835  suplem1pr 6313  pre-axsup 6444  ralbidar 16422  rexbidar 16423  smoge 16454

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

Copyright terms: Public domain