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Theorem anabsi5 521
Description: Absorption of antecedent into conjunction. (Contributed by NM, 11-Jun-1995.) (Proof shortened by Wolf Lammen, 18-Nov-2013.)
Hypothesis
Ref Expression
anabsi5.1  |-  ( ph  ->  ( ( ph  /\  ps )  ->  ch )
)
Assertion
Ref Expression
anabsi5  |-  ( (
ph  /\  ps )  ->  ch )

Proof of Theorem anabsi5
StepHypRef Expression
1 anabsi5.1 . . 3  |-  ( ph  ->  ( ( ph  /\  ps )  ->  ch )
)
21imp 119 . 2  |-  ( (
ph  /\  ( ph  /\ 
ps ) )  ->  ch )
32anabss5 520 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  anabsi6  522  anabsi8  524  3anidm12  1203  equsexd  1633  rspce  2668  phplem3g  6350  ltexprlemrl  6766  ltexprlemru  6768
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