Theorem simp31 991

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

Assertion

Ref	Expression
simp31	|- ((ph /\ ps /\ (ch /\ th /\ ta)) -> ch)

Proof of Theorem simp31

Step	Hyp	Ref	Expression
1		simp1 955	. 2 |- ((ch /\ th /\ ta) -> ch)
2	1	3ad2ant3 978	1 |- ((ph /\ ps /\ (ch /\ th /\ ta)) -> ch)

Syntax hints:   -> wi 4   /\ w3a 934

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is referenced by:  simpl31  1036  simpr31  1045  simp131  1090  simp231  1099  simp331  1108  tfin11  4494