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Theorem anabsi5 574
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 123 . 2  |-  ( (
ph  /\  ( ph  /\ 
ps ) )  ->  ch )
32anabss5 573 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  anabsi6  575  anabsi8  577  3anidm12  1290  equsexd  1722  rspce  2829  phplem3g  6831  ltexprlemrl  7561  ltexprlemru  7563  dvdssq  11975
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