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Theorem simp12 1012
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
Assertion
Ref Expression
simp12  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ps )

Proof of Theorem simp12
StepHypRef Expression
1 simp2 982 . 2  |-  ( (
ph  /\  ps  /\  ch )  ->  ps )
213ad2ant1 1002 1  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 962
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 964
This theorem is referenced by:  simpl12  1057  simpr12  1066  simp112  1111  simp212  1120  simp312  1129  frecsuclem  6303  dvdsgcd  11711
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