Theorem dfvd2ir 44539

Description: Right-to-left inference form of dfvd2 44532. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
dfvd2ir.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
dfvd2ir	⊢ (   𝜑   ,   𝜓   ▶   𝜒   )

Proof of Theorem dfvd2ir

Step	Hyp	Ref	Expression
1		dfvd2ir.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		dfvd2 44532	. 2 ⊢ ((   𝜑   ,   𝜓   ▶   𝜒   ) ↔ (𝜑 → (𝜓 → 𝜒)))
3	1, 2	mpbir 231	1 ⊢ (   𝜑   ,   𝜓   ▶   𝜒   )

Syntax hints:   → wi 4  (   wvd2 44530

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 207  df-an 396  df-vd2 44531

This theorem is referenced by:  vd02  44551  vd12  44553  in2an  44561  in3  44562  idn2  44566  gen21  44572  gen21nv  44573  gen22  44575  e2  44584  e222  44589