Theorem simplr2 1067

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 1031	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ps )
2	1	adantr 276	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ps )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1005

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 1007

This theorem is referenced by:  prarloclemlt  7824  prarloclemlo  7825  seq3f1oleml  10902  ccatswrd  11387  resqrexlemdecn  11722  pcdvdstr  13050  ennnfoneleminc  13246  grprcan  13792  mulgnn0dir  13905  prdssgrpd  14133  prdsmndd  14136  lmodprop2d  14622  lssintclm  14658  psrbaglesuppg  14947  restopnb  15172  cnptopresti  15229  blsscls2  15484