Theorem simp11 1011

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 981	. 2 |- ( ( ph /\ ps /\ ch ) -> ph )
2	1	3ad2ant1 1002	1 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ph )

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:  simpl11  1056  simpr11  1065  simp111  1110  simp211  1119  simp311  1128  frecsuclem  6296