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Theorem simp23 1032
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
Assertion
Ref Expression
simp23  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )  /\  ta )  ->  th )

Proof of Theorem simp23
StepHypRef Expression
1 simp3 999 . 2  |-  ( ( ps  /\  ch  /\  th )  ->  th )
213ad2ant2 1019 1  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )  /\  ta )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 980
This theorem is referenced by:  simpl23  1077  simpr23  1086  simp123  1131  simp223  1140  simp323  1149  funtpg  5259
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