Theorem simp31 1033

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

Assertion

Ref	Expression
simp31	|- ( ( ph /\ ps /\ ( ch /\ th /\ ta ) ) -> ch )

Proof of Theorem simp31

Step	Hyp	Ref	Expression
1		simp1 997	. 2 |- ( ( ch /\ th /\ ta ) -> ch )
2	1	3ad2ant3 1020	1 |- ( ( ph /\ ps /\ ( ch /\ th /\ ta ) ) -> ch )

Syntax hints:   -> wi 4   /\ w3a 978

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 980

This theorem is referenced by:  simpl31  1078  simpr31  1087  simp131  1132  simp231  1141  simp331  1150