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Theorem simpr3r 1017
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 984 . 2  |-  ( ( ch  /\  th  /\  ( ph  /\  ps )
)  ->  ps )
21adantl 452 1  |-  ( ( ta  /\  ( ch 
/\  th  /\  ( ph  /\  ps ) ) )  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934
This theorem is referenced by:  ax5seg  24566  segconeq  24633  ifscgr  24667  btwnconn1lem9  24718  btwnconn1lem11  24720  btwnconn1lem12  24721  lplnexllnN  29753  cdleme3b  30418  cdleme3c  30419  cdleme3e  30421  cdleme27a  30556
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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