Theorem simp21 937

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 904	. 2 |- ( ( ps /\ ch /\ th ) -> ps )
2	1	3ad2ant2 926	1 |- ( ( ph /\ ( ps /\ ch /\ th ) /\ ta ) -> ps )

Syntax hints:   -> wi 4   /\ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  simpl21  982  simpr21  991  simp121  1036  simp221  1045  simp321  1054