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Theorem simp321 1106
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp321  |-  ( ( et  /\  ze  /\  ( th  /\  ( ph  /\ 
ps  /\  ch )  /\  ta ) )  ->  ph )

Proof of Theorem simp321
StepHypRef Expression
1 simp21 989 . 2  |-  ( ( th  /\  ( ph  /\ 
ps  /\  ch )  /\  ta )  ->  ph )
213ad2ant3 979 1  |-  ( ( et  /\  ze  /\  ( th  /\  ( ph  /\ 
ps  /\  ch )  /\  ta ) )  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 935
This theorem is referenced by:  dalemcnes  29910  dalempnes  29911  dalemrot  29917  dath2  29997  cdleme18d  30555  cdleme20i  30577  cdleme20j  30578  cdleme20l2  30581  cdleme20l  30582  cdleme20m  30583  cdleme20  30584  cdleme21j  30596  cdleme22eALTN  30605  cdlemk16a  31116  cdlemk12u-2N  31150  cdlemk21-2N  31151  cdlemk22  31153  cdlemk31  31156  cdlemk32  31157  cdlemk11ta  31189  cdlemk11tc  31205
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 177  df-an 360  df-3an 937
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