Theorem simp12 1031

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 1001	. 2 |- ( ( ph /\ ps /\ ch ) -> ps )
2	1	3ad2ant1 1021	1 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ps )

Syntax hints:   -> wi 4   /\ w3a 981

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 983

This theorem is referenced by:  simpl12  1076  simpr12  1085  simp112  1130  simp212  1139  simp312  1148  frecsuclem  6492  dvdsgcd  12333  coprimeprodsq  12580  pythagtriplem4  12591  pythagtriplem13  12599  pythagtriplem14  12600  pythagtriplem16  12602  pythagtrip  12606  pceu  12618