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Theorem simp321 1146
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 1029 . 2  |-  ( ( th  /\  ( ph  /\ 
ps  /\  ch )  /\  ta )  ->  ph )
213ad2ant3 1019 1  |-  ( ( et  /\  ze  /\  ( th  /\  ( ph  /\ 
ps  /\  ch )  /\  ta ) )  ->  ph )
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:  dalemcnes  34446  dalempnes  34447  dalemrot  34453  dath2  34533  cdleme18d  35091  cdleme20i  35113  cdleme20j  35114  cdleme20l2  35117  cdleme20l  35118  cdleme20m  35119  cdleme20  35120  cdleme21j  35132  cdleme22eALTN  35141  cdlemk16a  35652  cdlemk12u-2N  35686  cdlemk21-2N  35687  cdlemk22  35689  cdlemk31  35692  cdlemk32  35693  cdlemk11ta  35725  cdlemk11tc  35741
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