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Theorem anabss5 789
Description: Absorption of antecedent into conjunction. (Contributed by NM, 10-May-1994.) (Proof shortened by Wolf Lammen, 1-Jan-2013.)
Hypothesis
Ref Expression
anabss5.1  |-  ( (
ph  /\  ( ph  /\ 
ps ) )  ->  ch )
Assertion
Ref Expression
anabss5  |-  ( (
ph  /\  ps )  ->  ch )

Proof of Theorem anabss5
StepHypRef Expression
1 anabss5.1 . . 3  |-  ( (
ph  /\  ( ph  /\ 
ps ) )  ->  ch )
21anassrs 629 . 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:  anabsi5  790  sq01  11223  faclbnd5  11311  hashssdif  11374  eqbrrdv2  26731  expgrowthi  27550  eel121  28491
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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