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Theorem simp31 1002
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
Assertion
Ref Expression
simp31  |-  ( (
ph  /\  ps  /\  ( ch  /\  th  /\  ta ) )  ->  ch )

Proof of Theorem simp31
StepHypRef Expression
1 simp1 966 . 2  |-  ( ( ch  /\  th  /\  ta )  ->  ch )
213ad2ant3 989 1  |-  ( (
ph  /\  ps  /\  ( ch  /\  th  /\  ta ) )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 947
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 949
This theorem is referenced by:  simpl31  1047  simpr31  1056  simp131  1101  simp231  1110  simp331  1119
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