Theorem simp12 1018

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 988	. 2 |- ( ( ph /\ ps /\ ch ) -> ps )
2	1	3ad2ant1 1008	1 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ps )

Syntax hints:   -> wi 4   /\ w3a 968

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 970

This theorem is referenced by:  simpl12  1063  simpr12  1072  simp112  1117  simp212  1126  simp312  1135  frecsuclem  6370  dvdsgcd  11941  coprimeprodsq  12185  pythagtriplem4  12196  pythagtriplem13  12204  pythagtriplem14  12205  pythagtriplem16  12207  pythagtrip  12211  pceu  12223