Theorem dfvd3ani 37008

Description: Inference form of dfvd3an 37007. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
dfvd3ani.1	|- (. (. ph ,. ps ,. ch ). ->. th ).

Assertion

Ref	Expression
dfvd3ani	|- ( ( ph /\ ps /\ ch ) -> th )

Proof of Theorem dfvd3ani

Step	Hyp	Ref	Expression
1		dfvd3ani.1	. 2 |- (. (. ph ,. ps ,. ch ). ->. th ).
2		dfvd3an 37007	. 2 |- ( (. (. ph ,. ps ,. ch ). ->. th ). <-> ( ( ph /\ ps /\ ch ) -> th ) )
3	1, 2	mpbi 213	1 |- ( ( ph /\ ps /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ w3a 991   (.wvd1 36982   (.wvhc3 37001

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 190  df-vd1 36983  df-vhc3 37002

This theorem is referenced by:  int3  37034  el0321old  37142