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Theorem simpr1l 996
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simpr1l  |-  ( ( ta  /\  ( (
ph  /\  ps )  /\  ch  /\  th )
)  ->  ph )

Proof of Theorem simpr1l
StepHypRef Expression
1 simp1l 963 . 2  |-  ( ( ( ph  /\  ps )  /\  ch  /\  th )  ->  ph )
21adantl 271 1  |-  ( ( ta  /\  ( (
ph  /\  ps )  /\  ch  /\  th )
)  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    /\ w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by:  prcdnql  6725  prnmaxl  6729
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