Theorem dfvd2anir 38800

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

Hypothesis

Ref	Expression
dfvd2anir.1	|- ( ( ph /\ ps ) -> ch )

Assertion

Ref	Expression
dfvd2anir	|- (. (. ph ,. ps ). ->. ch ).

Proof of Theorem dfvd2anir

Step	Hyp	Ref	Expression
1		dfvd2anir.1	. 2 |- ( ( ph /\ ps ) -> ch )
2		dfvd2an 38798	. 2 |- ( (. (. ph ,. ps ). ->. ch ). <-> ( ( ph /\ ps ) -> ch ) )
3	1, 2	mpbir 221	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:  int3  38837  el021old  38926  el2122old  38944  el12  38953