Theorem simp12 1028

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

Assertion

Ref	Expression
simp12	|- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ps )

Proof of Theorem simp12

Step	Hyp	Ref	Expression
1		simp2 998	. 2 |- ( ( ph /\ ps /\ ch ) -> ps )
2	1	3ad2ant1 1018	1 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ps )

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:  simpl12  1073  simpr12  1082  simp112  1127  simp212  1136  simp312  1145  frecsuclem  6409  dvdsgcd  12015  coprimeprodsq  12259  pythagtriplem4  12270  pythagtriplem13  12278  pythagtriplem14  12279  pythagtriplem16  12281  pythagtrip  12285  pceu  12297