Theorem simplr3 1072

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 1036	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ch )
2	1	adantr 276	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ch )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1009

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 1011

This theorem is referenced by:  netap  7610  prarloclemlt  7850  prarloclemlo  7851  ccatswrd  11420  pfxccat3  11484  resqrexlemdecn  11756  summodclem2  12127  isumss2  12138  pcdvdstr  13084  ennnfoneleminc  13280  grprcan  13819  mulgnn0dir  13932  mulgdir  13934  mulgass  13939  prdssgrpd  14168  prdsmndd  14171  lmodprop2d  14657  lssintclm  14693  psrbaglesuppg  14980  restopnb  15205  blsscls2  15517