Theorem simp13 996

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

Assertion

Ref	Expression
simp13	|- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ch )

Proof of Theorem simp13

Step	Hyp	Ref	Expression
1		simp3 966	. 2 |- ( ( ph /\ ps /\ ch ) -> ch )
2	1	3ad2ant1 985	1 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ch )

Syntax hints:   -> wi 4   /\ w3a 945

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 947

This theorem is referenced by:  simpl13  1041  simpr13  1050  simp113  1095  simp213  1104  simp313  1113  funtpg  5132  dvdsgcd  11543