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Theorem simpr3r 1020
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simpr3r  |-  ( ( ta  /\  ( ch 
/\  th  /\  ( ph  /\  ps ) ) )  ->  ps )

Proof of Theorem simpr3r
StepHypRef Expression
1 simp3r 987 . 2  |-  ( ( ch  /\  th  /\  ( ph  /\  ps )
)  ->  ps )
21adantl 454 1  |-  ( ( ta  /\  ( ch 
/\  th  /\  ( ph  /\  ps ) ) )  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360    /\ w3a 937
This theorem is referenced by:  ax5seg  25879  segconeq  25946  ifscgr  25980  btwnconn1lem9  26031  btwnconn1lem11  26033  btwnconn1lem12  26034  lplnexllnN  30423  cdleme3b  31088  cdleme3c  31089  cdleme3e  31091  cdleme27a  31226
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 179  df-an 362  df-3an 939
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