Theorem simp32 1029

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

Assertion

Ref	Expression
simp32	|- ( ( ph /\ ps /\ ( ch /\ th /\ ta ) ) -> th )

Proof of Theorem simp32

Step	Hyp	Ref	Expression
1		simp2 993	. 2 |- ( ( ch /\ th /\ ta ) -> th )
2	1	3ad2ant3 1015	1 |- ( ( ph /\ ps /\ ( ch /\ th /\ ta ) ) -> th )

Syntax hints:   -> wi 4   /\ w3a 973

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 975

This theorem is referenced by:  simpl32  1074  simpr32  1083  simp132  1128  simp232  1137  simp332  1146