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Theorem simpr3r 1059
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 1026 . 2  |-  ( ( ch  /\  th  /\  ( ph  /\  ps )
)  ->  ps )
21adantl 466 1  |-  ( ( ta  /\  ( ch 
/\  th  /\  ( ph  /\  ps ) ) )  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    /\ w3a 974
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 976
This theorem is referenced by:  ax5seg  24113  segconeq  29635  ifscgr  29669  btwnconn1lem9  29720  btwnconn1lem11  29722  btwnconn1lem12  29723  lplnexllnN  35028  cdleme3b  35694  cdleme3c  35695  cdleme3e  35697  cdleme27a  35833
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