Theorem simp22 972

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

Assertion

Ref	Expression
simp22	|- ( ( ph /\ ( ps /\ ch /\ th ) /\ ta ) -> ch )

Proof of Theorem simp22

Step	Hyp	Ref	Expression
1		simp2 939	. 2 |- ( ( ps /\ ch /\ th ) -> ch )
2	1	3ad2ant2 960	1 |- ( ( ph /\ ( ps /\ ch /\ th ) /\ ta ) -> ch )

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:  simpl22  1017  simpr22  1026  simp122  1071  simp222  1080  simp322  1089  prarloclem5  6690