Theorem simpr31 1028

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

Assertion

Ref	Expression
simpr31	|- ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) ) -> ph )

Proof of Theorem simpr31

Step	Hyp	Ref	Expression
1		simp31 974	. 2 |- ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) -> ph )
2	1	adantl 271	1 |- ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) ) -> ph )

Syntax hints:   -> wi 4   /\ wa 102   /\ w3a 919

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-3an 921

This theorem is referenced by: (None)