Theorem simplr2 1071

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 1035	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ps )
2	1	adantr 276	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ps )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  prarloclemlt  7861  prarloclemlo  7862  seq3f1oleml  10968  ccatswrd  11458  resqrexlemdecn  11794  pcdvdstr  13129  ennnfoneleminc  13354  grprcan  13895  mulgnn0dir  14008  prdssgrpd  14275  prdsmndd  14278  lmodprop2d  14769  lssintclm  14805  psrbaglesuppg  15141  restopnb  15373  cnptopresti  15430  blsscls2  15685