Theorem simp12 1059

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 1029	. 2 |- ( ( ph /\ ps /\ ch ) -> ps )
2	1	3ad2ant1 1049	1 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ps )

This proof depends on syntax axioms:   -> wi 4   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  simpl12  1104  simpr12  1113  simp112  1158  simp212  1167  simp312  1176  frecsuclem  6677  dvdsgcd  12789  coprimeprodsq  13036  pythagtriplem4  13047  pythagtriplem13  13055  pythagtriplem14  13056  pythagtriplem16  13058  pythagtrip  13062  pceu  13074