Theorem simp13 1029

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 999	. 2 |- ( ( ph /\ ps /\ ch ) -> ch )
2	1	3ad2ant1 1018	1 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ch )

Syntax hints:   -> wi 4   /\ w3a 978

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 980

This theorem is referenced by:  simpl13  1074  simpr13  1083  simp113  1128  simp213  1137  simp313  1146  funtpg  5269  dvdsgcd  12015  coprimeprodsq  12259  pythagtriplem4  12270  pythagtriplem13  12278  pythagtriplem14  12279  pythagtriplem16  12281  pythagtrip  12285