Theorem simp31 1023

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 987	. 2 |- ( ( ch /\ th /\ ta ) -> ch )
2	1	3ad2ant3 1010	1 |- ( ( ph /\ ps /\ ( ch /\ th /\ ta ) ) -> ch )

Syntax hints:   -> wi 4   /\ w3a 968

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 970

This theorem is referenced by:  simpl31  1068  simpr31  1077  simp131  1122  simp231  1131  simp331  1140