Theorem simp21 1030

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

Assertion

Ref	Expression
simp21	|- ( ( ph /\ ( ps /\ ch /\ th ) /\ ta ) -> ps )

Proof of Theorem simp21

Step	Hyp	Ref	Expression
1		simp1 997	. 2 |- ( ( ps /\ ch /\ th ) -> ps )
2	1	3ad2ant2 1019	1 |- ( ( ph /\ ( ps /\ ch /\ th ) /\ ta ) -> ps )

Syntax hints:   -> wi 4   /\ w3a 978

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 980

This theorem is referenced by:  simpl21  1075  simpr21  1084  simp121  1129  simp221  1138  simp321  1147  mulgdirlem  13019