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Theorem anabss5 824
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 653 . 2  |-  ( ( ( ph  /\  ph )  /\  ps )  ->  ch )
32anabsan 821 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 371
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 189  df-an 373
This theorem is referenced by:  anabsi5  825  sq01  12395  faclbnd5  12484  hashssdif  12588  eqbrrdv2  32359  expgrowthi  36546  bccbc  36558  eel0121  36956  eel121  36963
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