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Theorem simp321 1147
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 1030 . 2  |-  ( ( th  /\  ( ph  /\ 
ps  /\  ch )  /\  ta )  ->  ph )
213ad2ant3 1020 1  |-  ( ( et  /\  ze  /\  ( th  /\  ( ph  /\ 
ps  /\  ch )  /\  ta ) )  ->  ph )
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:  dalemcnes  32647  dalempnes  32648  dalemrot  32654  dath2  32734  cdleme18d  33293  cdleme20i  33316  cdleme20j  33317  cdleme20l2  33320  cdleme20l  33321  cdleme20m  33322  cdleme20  33323  cdleme21j  33335  cdleme22eALTN  33344  cdlemk16a  33855  cdlemk12u-2N  33889  cdlemk21-2N  33890  cdlemk22  33892  cdlemk31  33895  cdlemk32  33896  cdlemk11ta  33928  cdlemk11tc  33944
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