Theorem simp11 1029

Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)

Assertion

Ref	Expression
simp11	|- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ph )

Proof of Theorem simp11

Step	Hyp	Ref	Expression
1		simp1 999	. 2 |- ( ( ph /\ ps /\ ch ) -> ph )
2	1	3ad2ant1 1020	1 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ph )

Syntax hints:   -> wi 4   /\ w3a 980

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 982

This theorem is referenced by:  simpl11  1074  simpr11  1083  simp111  1128  simp211  1137  simp311  1146  frecsuclem  6464  coprimeprodsq  12426  pythagtriplem14  12446  pythagtrip  12452