Theorem 3anibar

Description: Remove a hypothesis from the second member of a biconditional. (Contributed by FL, 22-Jul-2008)

	Ref	Expression
Hypothesis	3anibar.1	|- ( ( ph /\ ps /\ ch ) -> ( th <-> ( ch /\ ta ) ) )
Assertion	3anibar	|- ( ( ph /\ ps /\ ch ) -> ( th <-> ta ) )

Proof

Step	Hyp	Ref	Expression
1		3anibar.1	|- ( ( ph /\ ps /\ ch ) -> ( th <-> ( ch /\ ta ) ) )
2		simp3	|- ( ( ph /\ ps /\ ch ) -> ch )
3	2 1	mpbirand	|- ( ( ph /\ ps /\ ch ) -> ( th <-> ta ) )