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Theorem simp312 1105
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 988 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ps )
213ad2ant3 980 1  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 936
This theorem is referenced by:  dalemrot  29773  dalem-cly  29787  dath2  29853  cdleme26e  30475  cdleme38m  30579  cdleme38n  30580  cdleme39n  30582  cdlemg28b  30819  cdlemk7  30964  cdlemk11  30965  cdlemk12  30966  cdlemk7u  30986  cdlemk11u  30987  cdlemk12u  30988  cdlemk22  31009  cdlemk23-3  31018  cdlemk25-3  31020
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  df-3an 938
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