Theorem simp13 970

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 940	. 2 |- ( ( ph /\ ps /\ ch ) -> ch )
2	1	3ad2ant1 959	1 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ch )

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:  simpl13  1015  simpr13  1024  simp113  1069  simp213  1078  simp313  1087  funtpg  4970  dvdsgcd  10401