Theorem simpl3r 1056

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simpl3r	|- ( ( ( ch /\ th /\ ( ph /\ ps ) ) /\ ta ) -> ps )

Proof of Theorem simpl3r

Step	Hyp	Ref	Expression
1		simp3r 1029	. 2 |- ( ( ch /\ th /\ ( ph /\ ps ) ) -> ps )
2	1	adantr 276	1 |- ( ( ( ch /\ th /\ ( ph /\ ps ) ) /\ ta ) -> ps )

Syntax hints:   -> wi 4   /\ wa 104   /\ 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:  tfisi  4653  ltmul1a  8699  lemul1a  8966  swrdsbslen  11157  swrdspsleq  11158  xrbdtri  11702  dvdscmulr  12246  dvdsmulcr  12247  dvdsadd2b  12266  pockthg  12795