Theorem simplr1 1041

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simplr1	|- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ph )

Proof of Theorem simplr1

Step	Hyp	Ref	Expression
1		simpr1 1005	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ph )
2	1	adantr 276	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ph )

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  7337  prarloclemlt  7577  prarloclemlo  7578  summodclem2  11564  pcdvdstr  12521  prdssgrpd  13117  prdsmndd  13150  grprcan  13239  lmodprop2d  13980  lssintclm  14016  psrbaglesuppg  14302  restopnb  14501  blsscls2  14813