Theorem simp33 976

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

Assertion

Ref	Expression
simp33	|- ( ( ph /\ ps /\ ( ch /\ th /\ ta ) ) -> ta )

Proof of Theorem simp33

Step	Hyp	Ref	Expression
1		simp3 940	. 2 |- ( ( ch /\ th /\ ta ) -> ta )
2	1	3ad2ant3 961	1 |- ( ( ph /\ ps /\ ( ch /\ th /\ ta ) ) -> ta )

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:  simpl33  1021  simpr33  1030  simp133  1075  simp233  1084  simp333  1093