Theorem simp12 980

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 950	. 2 |- ( ( ph /\ ps /\ ch ) -> ps )
2	1	3ad2ant1 970	1 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ps )

Syntax hints:   -> wi 4   /\ w3a 930

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

This theorem depends on definitions:  df-bi 116  df-3an 932

This theorem is referenced by:  simpl12  1025  simpr12  1034  simp112  1079  simp212  1088  simp312  1097  frecsuclem  6233  dvdsgcd  11493