Theorem simp11 968

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 938	. 2 |- ( ( ph /\ ps /\ ch ) -> ph )
2	1	3ad2ant1 959	1 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ph )

Syntax hints:   -> wi 4   /\ w3a 919

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-3an 921

This theorem is referenced by:  simpl11  1013  simpr11  1022  simp111  1067  simp211  1076  simp311  1085