Theorem simp23 1022

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

Assertion

Ref	Expression
simp23	|- ( ( ph /\ ( ps /\ ch /\ th ) /\ ta ) -> th )

Proof of Theorem simp23

Step	Hyp	Ref	Expression
1		simp3 989	. 2 |- ( ( ps /\ ch /\ th ) -> th )
2	1	3ad2ant2 1009	1 |- ( ( ph /\ ( ps /\ ch /\ th ) /\ ta ) -> th )

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:  simpl23  1067  simpr23  1076  simp123  1121  simp223  1130  simp323  1139  funtpg  5239