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  7316  prarloclemlt  7555  prarloclemlo  7556  resqrexlemdecn  11159  summodclem2  11528  isumss2  11539  pcdvdstr  12468  ennnfoneleminc  12571  grprcan  13112  mulgnn0dir  13225  mulgdir  13227  mulgass  13232  lmodprop2d  13847  lssintclm  13883  psrbaglesuppg  14169  restopnb  14360  blsscls2  14672