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Theorem simpr32 1048
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simpr32  |-  ( ( et  /\  ( th 
/\  ta  /\  ( ph  /\  ps  /\  ch ) ) )  ->  ps )

Proof of Theorem simpr32
StepHypRef Expression
1 simp32 994 . 2  |-  ( ( th  /\  ta  /\  ( ph  /\  ps  /\  ch ) )  ->  ps )
21adantl 453 1  |-  ( ( et  /\  ( th 
/\  ta  /\  ( ph  /\  ps  /\  ch ) ) )  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359    /\ w3a 936
This theorem is referenced by:  oppccatid  13933  subccatid  14031  fuccatid  14154  setccatid  14227  catccatid  14245  xpccatid  14273  nllyidm  17540  utoptop  18252  cgr3tr4  25934  paddasslem9  30464  cdlemd1  30834  cdlemf2  31198  cdlemk34  31546  dihmeetlem18N  31961
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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