Theorem simplr3 1065

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 1029	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ch )
2	1	adantr 276	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ch )

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:  netap  7436  prarloclemlt  7676  prarloclemlo  7677  ccatswrd  11197  pfxccat3  11261  resqrexlemdecn  11518  summodclem2  11888  isumss2  11899  pcdvdstr  12845  ennnfoneleminc  12977  prdssgrpd  13443  prdsmndd  13476  grprcan  13565  mulgnn0dir  13684  mulgdir  13686  mulgass  13691  lmodprop2d  14306  lssintclm  14342  psrbaglesuppg  14630  restopnb  14849  blsscls2  15161