Theorem dfvd2i 43346

Description: Inference form of dfvd2 43340. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
dfvd2i.1	⊢ (   𝜑   ,   𝜓   ▶   𝜒   )

Assertion

Ref	Expression
dfvd2i	⊢ (𝜑 → (𝜓 → 𝜒))

Proof of Theorem dfvd2i

Step	Hyp	Ref	Expression
1		dfvd2i.1	. 2 ⊢ (   𝜑   ,   𝜓   ▶   𝜒   )
2		dfvd2 43340	. 2 ⊢ ((   𝜑   ,   𝜓   ▶   𝜒   ) ↔ (𝜑 → (𝜓 → 𝜒)))
3	1, 2	mpbi 229	1 ⊢ (𝜑 → (𝜓 → 𝜒))

Syntax hints:   → wi 4  (   wvd2 43338

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 206  df-an 398  df-vd2 43339

This theorem is referenced by:  vd23  43363  in2  43366  in2an  43369  gen21  43380  gen21nv  43381  gen22  43383  exinst  43385  exinst01  43386  exinst11  43387  e2  43392  e222  43397  e233  43526  e323  43527