Theorem simplr2 1042

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 1006	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ps )
2	1	adantr 276	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ps )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 980

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 982

This theorem is referenced by:  prarloclemlt  7562  prarloclemlo  7563  seq3f1oleml  10610  resqrexlemdecn  11179  pcdvdstr  12506  ennnfoneleminc  12638  grprcan  13179  mulgnn0dir  13292  lmodprop2d  13914  lssintclm  13950  psrbaglesuppg  14236  restopnb  14427  cnptopresti  14484  blsscls2  14739