Theorem simp12 1030

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 1000	. 2 |- ( ( ph /\ ps /\ ch ) -> ps )
2	1	3ad2ant1 1020	1 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ps )

Syntax hints:   -> wi 4   /\ w3a 980

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 982

This theorem is referenced by:  simpl12  1075  simpr12  1084  simp112  1129  simp212  1138  simp312  1147  frecsuclem  6430  dvdsgcd  12044  coprimeprodsq  12288  pythagtriplem4  12299  pythagtriplem13  12307  pythagtriplem14  12308  pythagtriplem16  12310  pythagtrip  12314  pceu  12326