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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  |-  ( (
ph  ->  ( ph  ->  ps ) )  ->  ( ph  ->  ps ) )

Proof of Theorem pm2.43
StepHypRef Expression
1 pm2.27 35 . 2  |-  ( ph  ->  ( ( ph  ->  ps )  ->  ps )
)
21a2i 12 1  |-  ( (
ph  ->  ( ph  ->  ps ) )  ->  ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  pm5.4  351  tfrlem1  6407  ralbidar  27751  rexbidar  27752
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
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