Theorem simp11 1058

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 1028	. 2 |- ( ( ph /\ ps /\ ch ) -> ph )
2	1	3ad2ant1 1049	1 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ph )

This proof depends on syntax axioms:   -> wi 4   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  simpl11  1103  simpr11  1112  simp111  1157  simp211  1166  simp311  1175  frecsuclem  6677  coprimeprodsq  13036  pythagtriplem14  13056  pythagtrip  13062  clwwlknonex2  16680