Theorem dfvd2ani 38799

Description: Inference form of dfvd2an 38798. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
dfvd2ani.1	|- (. (. ph ,. ps ). ->. ch ).

Assertion

Ref	Expression
dfvd2ani	|- ( ( ph /\ ps ) -> ch )

Proof of Theorem dfvd2ani

Step	Hyp	Ref	Expression
1		dfvd2ani.1	. 2 |- (. (. ph ,. ps ). ->. ch ).
2		dfvd2an 38798	. 2 |- ( (. (. ph ,. ps ). ->. ch ). <-> ( ( ph /\ ps ) -> ch ) )
3	1, 2	mpbi 220	1 |- ( ( ph /\ ps ) -> ch )

Syntax hints:   -> wi 4   /\ wa 384   (.wvd1 38785   (.wvhc2 38796

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 197  df-vd1 38786  df-vhc2 38797

This theorem is referenced by:  int2  38831  el021old  38926  el2122old  38944  un0.1  39006  un10  39015  un01  39016