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Theorem anabss3 819
Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 1-Jan-2013.)
Hypothesis
Ref Expression
anabss3.1  |-  ( ( ( ph  /\  ps )  /\  ps )  ->  ch )
Assertion
Ref Expression
anabss3  |-  ( (
ph  /\  ps )  ->  ch )

Proof of Theorem anabss3
StepHypRef Expression
1 anabss3.1 . . 3  |-  ( ( ( ph  /\  ps )  /\  ps )  ->  ch )
21anasss 647 . 2  |-  ( (
ph  /\  ( ps  /\ 
ps ) )  ->  ch )
32anabsan2 818 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369
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 185  df-an 371
This theorem is referenced by:  3anidm23  1278  expclzlem  12001  plyrem  21899  anabss7p1  31833
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