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Theorem pm5.4 351
Description: Antecedent absorption implication. Theorem *5.4 of [WhiteheadRussell] p. 125. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
pm5.4  |-  ( (
ph  ->  ( ph  ->  ps ) )  <->  ( ph  ->  ps ) )

Proof of Theorem pm5.4
StepHypRef Expression
1 pm2.43 47 . 2  |-  ( (
ph  ->  ( ph  ->  ps ) )  ->  ( ph  ->  ps ) )
2 ax-1 5 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ( ph  ->  ps ) ) )
31, 2impbii 180 1  |-  ( (
ph  ->  ( ph  ->  ps ) )  <->  ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176
This theorem is referenced by:  moabs  2189
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177
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