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  7712  prarloclemlo  7713  seq3f1oleml  10777  ccatswrd  11250  resqrexlemdecn  11572  pcdvdstr  12899  ennnfoneleminc  13031  prdssgrpd  13497  prdsmndd  13530  grprcan  13619  mulgnn0dir  13738  lmodprop2d  14361  lssintclm  14397  psrbaglesuppg  14685  restopnb  14904  cnptopresti  14961  blsscls2  15216