Theorem simplr1 1065

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

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  summodclem2  11942  pcdvdstr  12899  prdssgrpd  13497  prdsmndd  13530  grprcan  13619  lmodprop2d  14361  lssintclm  14397  psrbaglesuppg  14685  restopnb  14904  blsscls2  15216