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Theorem simpr11 1078
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simpr11  |-  ( ( et  /\  ( (
ph  /\  ps  /\  ch )  /\  th  /\  ta ) )  ->  ph )

Proof of Theorem simpr11
StepHypRef Expression
1 simp11 1024 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ph )
21adantl 464 1  |-  ( ( et  /\  ( (
ph  /\  ps  /\  ch )  /\  th  /\  ta ) )  ->  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367    /\ w3a 971
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 369  df-3an 973
This theorem is referenced by:  el2spthonot0  25017  cgr3tr4  29895  btwnoutside  29968  paddasslem8  36003  cdleme27a  36545
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