Theorem simp11 1022

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 992	. 2 |- ( ( ph /\ ps /\ ch ) -> ph )
2	1	3ad2ant1 1013	1 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ph )

Syntax hints:   -> wi 4   /\ w3a 973

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 975

This theorem is referenced by:  simpl11  1067  simpr11  1076  simp111  1121  simp211  1130  simp311  1139  frecsuclem  6385  coprimeprodsq  12211  pythagtriplem14  12231  pythagtrip  12237