Theorem simplr3 1067

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 1031	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ch )
2	1	adantr 276	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ch )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1004

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 1006

This theorem is referenced by:  netap  7472  prarloclemlt  7712  prarloclemlo  7713  ccatswrd  11250  pfxccat3  11314  resqrexlemdecn  11572  summodclem2  11942  isumss2  11953  pcdvdstr  12899  ennnfoneleminc  13031  prdssgrpd  13497  prdsmndd  13530  grprcan  13619  mulgnn0dir  13738  mulgdir  13740  mulgass  13745  lmodprop2d  14361  lssintclm  14397  psrbaglesuppg  14685  restopnb  14904  blsscls2  15216