Theorem simpr1r 1045

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

Assertion

Ref	Expression
simpr1r	|- ( ( ta /\ ( ( ph /\ ps ) /\ ch /\ th ) ) -> ps )

Proof of Theorem simpr1r

Step	Hyp	Ref	Expression
1		simp1r 1012	. 2 |- ( ( ( ph /\ ps ) /\ ch /\ th ) -> ps )
2	1	adantl 275	1 |- ( ( ta /\ ( ( ph /\ ps ) /\ ch /\ th ) ) -> ps )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 968

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 970

This theorem is referenced by:  prcunqu  7426  prnminu  7430  neitx  12918