Theorem dfvd3anir 36377

Description: Right-to-left inference form of dfvd3an 36375. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

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

Assertion

Ref	Expression
dfvd3anir	|- (. (. ph ,. ps ,. ch ). ->. th ).

Proof of Theorem dfvd3anir

Step	Hyp	Ref	Expression
1		dfvd3anir.1	. 2 |- ( ( ph /\ ps /\ ch ) -> th )
2		dfvd3an 36375	. 2 |- ( (. (. ph ,. ps ,. ch ). ->. th ). <-> ( ( ph /\ ps /\ ch ) -> th ) )
3	1, 2	mpbir 209	1 |- (. (. ph ,. ps ,. ch ). ->. th ).

Syntax hints:   -> wi 4   /\ w3a 974   (.wvd1 36350   (.wvhc3 36369

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 185  df-vd1 36351  df-vhc3 36370

This theorem is referenced by:  el0321old  36516  el123  36565