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Theorem anabsan 820
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 pm4.24 647 . 2  |-  ( ph  <->  (
ph  /\  ph ) )
2 anabsan.1 . 2  |-  ( ( ( ph  /\  ph )  /\  ps )  ->  ch )
31, 2sylanb 474 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 370
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 188  df-an 372
This theorem is referenced by:  anabss1  821  anabss5  823  anandis  837  iddvds  14259  1dvds  14260
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