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Theorem simpr12 1040
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simpr12  |-  ( ( et  /\  ( (
ph  /\  ps  /\  ch )  /\  th  /\  ta ) )  ->  ps )

Proof of Theorem simpr12
StepHypRef Expression
1 simp12 986 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ps )
21adantl 452 1  |-  ( ( et  /\  ( (
ph  /\  ps  /\  ch )  /\  th  /\  ta ) )  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934
This theorem is referenced by:  cgr3tr4  24747  btwnoutside  24820  paddasslem8  30638  cdleme27a  31178
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 936
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