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Theorem pm5.4 248
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 53 . 2  |-  ( (
ph  ->  ( ph  ->  ps ) )  ->  ( ph  ->  ps ) )
2 ax-1 6 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ( ph  ->  ps ) ) )
31, 2impbii 125 1  |-  ( (
ph  ->  ( ph  ->  ps ) )  <->  ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  sbequ8  1819  moabs  2048  rgenm  3465  isprm4  11800  limcdifap  12800
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