Theorem simp13 1031

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 1001	. 2 |- ( ( ph /\ ps /\ ch ) -> ch )
2	1	3ad2ant1 1020	1 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ch )

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:  simpl13  1076  simpr13  1085  simp113  1130  simp213  1139  simp313  1148  funtpg  5305  dvdsgcd  12149  coprimeprodsq  12395  pythagtriplem4  12406  pythagtriplem13  12414  pythagtriplem14  12415  pythagtriplem16  12417  pythagtrip  12421