Theorem simp33 1037

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 1001	. 2 |- ( ( ch /\ th /\ ta ) -> ta )
2	1	3ad2ant3 1022	1 |- ( ( ph /\ ps /\ ( ch /\ th /\ ta ) ) -> ta )

Syntax hints:   -> wi 4   /\ w3a 980

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 982

This theorem is referenced by:  simpl33  1082  simpr33  1091  simp133  1136  simp233  1145  simp333  1154  bitsfzo  12119