Theorem dfvd2i 45161

Description: Inference form of dfvd2 45155. (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 45155	. 2 ⊢ ((   𝜑   ,   𝜓   ▶   𝜒   ) ↔ (𝜑 → (𝜓 → 𝜒)))
3	1, 2	mpbi 232	1 ⊢ (𝜑 → (𝜓 → 𝜒))

Syntax hints:   → wi 4  (   wvd2 45153

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 209  df-an 400  df-vd2 45154

This theorem is referenced by:  vd23  45178  in2  45181  in2an  45184  gen21  45195  gen21nv  45196  gen22  45198  exinst  45200  exinst01  45201  exinst11  45202  e2  45207  e222  45212  e233  45340  e323  45341