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Theorem anabss7 795
Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 19-Nov-2013.)
Hypothesis
Ref Expression
anabss7.1  |-  ( ( ps  /\  ( ph  /\ 
ps ) )  ->  ch )
Assertion
Ref Expression
anabss7  |-  ( (
ph  /\  ps )  ->  ch )

Proof of Theorem anabss7
StepHypRef Expression
1 anabss7.1 . . 3  |-  ( ( ps  /\  ( ph  /\ 
ps ) )  ->  ch )
21anassrs 630 . 2  |-  ( ( ( ps  /\  ph )  /\  ps )  ->  ch )
32anabss4 789 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359
This theorem is referenced by:  anabsan2  796  funbrfv  5765  faclbnd5  11589  divalgmod  12926  eel221  28825
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 178  df-an 361
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