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  7365  prarloclemlt  7605  prarloclemlo  7606  resqrexlemdecn  11265  summodclem2  11635  isumss2  11646  pcdvdstr  12592  ennnfoneleminc  12724  prdssgrpd  13189  prdsmndd  13222  grprcan  13311  mulgnn0dir  13430  mulgdir  13432  mulgass  13437  lmodprop2d  14052  lssintclm  14088  psrbaglesuppg  14376  restopnb  14595  blsscls2  14907