Theorem simpr32 1078

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

Assertion

Ref	Expression
simpr32	|- ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) ) -> ps )

Proof of Theorem simpr32

Step	Hyp	Ref	Expression
1		simp32 1024	. 2 |- ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) -> ps )
2	1	adantl 275	1 |- ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) ) -> 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: (None)