Theorem simplr1 1034

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 998	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ph )
2	1	adantr 274	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ph )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 973

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 975

This theorem is referenced by:  prarloclemlt  7455  prarloclemlo  7456  summodclem2  11345  pcdvdstr  12280  grprcan  12740  restopnb  12975  blsscls2  13287