Theorem simplr2 1066

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

Assertion

Ref	Expression
simplr2	|- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ps )

Proof of Theorem simplr2

Step	Hyp	Ref	Expression
1		simpr2 1030	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ps )
2	1	adantr 276	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ps )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1004

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 1006

This theorem is referenced by:  prarloclemlt  7713  prarloclemlo  7714  seq3f1oleml  10779  ccatswrd  11255  resqrexlemdecn  11590  pcdvdstr  12918  ennnfoneleminc  13050  prdssgrpd  13516  prdsmndd  13549  grprcan  13638  mulgnn0dir  13757  lmodprop2d  14381  lssintclm  14417  psrbaglesuppg  14705  restopnb  14924  cnptopresti  14981  blsscls2  15236