Theorem dfvd3ir 38809

Description: Right-to-left inference form of dfvd3 38807. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
dfvd3ir.1	|- ( ph -> ( ps -> ( ch -> th ) ) )

Assertion

Ref	Expression
dfvd3ir	|- (. ph ,. ps ,. ch ->. th ).

Proof of Theorem dfvd3ir

Step	Hyp	Ref	Expression
1		dfvd3ir.1	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
2		dfvd3 38807	. 2 |- ( (. ph ,. ps ,. ch ->. th ). <-> ( ph -> ( ps -> ( ch -> th ) ) ) )
3	1, 2	mpbir 221	1 |- (. ph ,. ps ,. ch ->. th ).

Syntax hints:   -> wi 4   (.wvd3 38803

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-an 386  df-3an 1039  df-vd3 38806

This theorem is referenced by:  vd03  38824  vd13  38826  vd23  38827  in3an  38836  idn3  38840  gen31  38846  e223  38860  e333  38960  e233  38992  e323  38993