Theorem dfvd3ani 33785

Description: Inference form of dfvd3an 33784. (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 33784	. 2 |- ( (. (. ph ,. ps ,. ch ). ->. th ). <-> ( ( ph /\ ps /\ ch ) -> th ) )
3	1, 2	mpbi 208	1 |- ( ( ph /\ ps /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ w3a 971   (.wvd1 33759   (.wvhc3 33778

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 33760  df-vhc3 33779

This theorem is referenced by:  int3  33811  el0321old  33925