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Theorem anabss1 787
Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 31-Dec-2012.)
Hypothesis
Ref Expression
anabss1.1  |-  ( ( ( ph  /\  ps )  /\  ph )  ->  ch )
Assertion
Ref Expression
anabss1  |-  ( (
ph  /\  ps )  ->  ch )

Proof of Theorem anabss1
StepHypRef Expression
1 anabss1.1 . . 3  |-  ( ( ( ph  /\  ps )  /\  ph )  ->  ch )
21an32s 779 . 2  |-  ( ( ( ph  /\  ph )  /\  ps )  ->  ch )
32anabsan 786 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  anabss4  788  ordtri3or  4424  onfununi  6358  omordi  6564  oeoelem  6596  hashssdif  11374
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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