Theorem dfvd3anir

Description: Right-to-left inference form of dfvd3an . (Contributed by Alan Sare, 13-Jun-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	dfvd3anir.1	|- ( ( ph /\ ps /\ ch ) -> th )
Assertion	dfvd3anir	|- (. (. ph ,. ps ,. ch ). ->. th ).

Proof

Step	Hyp	Ref	Expression
1		dfvd3anir.1	|- ( ( ph /\ ps /\ ch ) -> th )
2		dfvd3an	|- ( (. (. ph ,. ps ,. ch ). ->. th ). <-> ( ( ph /\ ps /\ ch ) -> th ) )
3	1 2	mpbir	|- (. (. ph ,. ps ,. ch ). ->. th ).