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Theorem simp33 987
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
Assertion
Ref Expression
simp33  |-  ( (
ph  /\  ps  /\  ( ch  /\  th  /\  ta ) )  ->  ta )

Proof of Theorem simp33
StepHypRef Expression
1 simp3 951 . 2  |-  ( ( ch  /\  th  /\  ta )  ->  ta )
213ad2ant3 972 1  |-  ( (
ph  /\  ps  /\  ( ch  /\  th  /\  ta ) )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 930
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 932
This theorem is referenced by:  simpl33  1032  simpr33  1041  simp133  1086  simp233  1095  simp333  1104
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