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Theorem simp312 1144
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 1027 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ps )
213ad2ant3 1019 1  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ w3a 973
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  df-3an 975
This theorem is referenced by:  dalemrot  34453  dalem-cly  34467  dath2  34533  cdleme26e  35155  cdleme38m  35259  cdleme38n  35260  cdleme39n  35262  cdlemg28b  35499  cdlemk7  35644  cdlemk11  35645  cdlemk12  35646  cdlemk7u  35666  cdlemk11u  35667  cdlemk12u  35668  cdlemk22  35689  cdlemk23-3  35698  cdlemk25-3  35700
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