Theorem simp22 1055

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 1022	. 2 |- ( ( ps /\ ch /\ th ) -> ch )
2	1	3ad2ant2 1043	1 |- ( ( ph /\ ( ps /\ ch /\ th ) /\ ta ) -> ch )

Syntax hints:   -> wi 4   /\ w3a 1002

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 1004

This theorem is referenced by:  simpl22  1100  simpr22  1109  simp122  1154  simp222  1163  simp322  1172  prarloclem5  7687  mulgdirlem  13690