Theorem simplr3 1043

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simplr3	|- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ch )

Proof of Theorem simplr3

Step	Hyp	Ref	Expression
1		simpr3 1007	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ch )
2	1	adantr 276	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ch )

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:  netap  7271  prarloclemlt  7510  prarloclemlo  7511  resqrexlemdecn  11039  summodclem2  11408  isumss2  11419  pcdvdstr  12344  ennnfoneleminc  12430  grprcan  12947  mulgnn0dir  13058  mulgdir  13060  mulgass  13065  lmodprop2d  13625  lssintclm  13661  restopnb  14078  blsscls2  14390