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Theorem simp312 1145
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp312  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ps )

Proof of Theorem simp312
StepHypRef Expression
1 simp12 1028 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ps )
213ad2ant3 1020 1  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ w3a 974
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 369  df-3an 976
This theorem is referenced by:  dalemrot  32655  dalem-cly  32669  dath2  32735  cdleme26e  33359  cdleme38m  33463  cdleme38n  33464  cdleme39n  33466  cdlemg28b  33703  cdlemk7  33848  cdlemk11  33849  cdlemk12  33850  cdlemk7u  33870  cdlemk11u  33871  cdlemk12u  33872  cdlemk22  33893  cdlemk23-3  33902  cdlemk25-3  33904
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