Theorem simplr2 1064

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 1028	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ps )
2	1	adantr 276	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ps )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1002

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 1004

This theorem is referenced by:  prarloclemlt  7703  prarloclemlo  7704  seq3f1oleml  10768  ccatswrd  11241  resqrexlemdecn  11563  pcdvdstr  12890  ennnfoneleminc  13022  prdssgrpd  13488  prdsmndd  13521  grprcan  13610  mulgnn0dir  13729  lmodprop2d  14352  lssintclm  14388  psrbaglesuppg  14676  restopnb  14895  cnptopresti  14952  blsscls2  15207