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Theorem anabsan 786
Description: Absorption of antecedent with conjunction. (Contributed by NM, 24-Mar-1996.)
Hypothesis
Ref Expression
anabsan.1  |-  ( ( ( ph  /\  ph )  /\  ps )  ->  ch )
Assertion
Ref Expression
anabsan  |-  ( (
ph  /\  ps )  ->  ch )

Proof of Theorem anabsan
StepHypRef Expression
1 pm4.24 624 . 2  |-  ( ph  <->  (
ph  /\  ph ) )
2 anabsan.1 . 2  |-  ( ( ( ph  /\  ph )  /\  ps )  ->  ch )
31, 2sylanb 458 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  anabss1  787  anabss5  789  anandis  803  iddvds  12558  1dvds  12559
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  df-an 360
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