Theorem dfvd2i 44548

Description: Inference form of dfvd2 44542. (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 44542	. 2 ⊢ ((   𝜑   ,   𝜓   ▶   𝜒   ) ↔ (𝜑 → (𝜓 → 𝜒)))
3	1, 2	mpbi 230	1 ⊢ (𝜑 → (𝜓 → 𝜒))

Syntax hints:   → wi 4  (   wvd2 44540

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 44541

This theorem is referenced by:  vd23  44565  in2  44568  in2an  44571  gen21  44582  gen21nv  44583  gen22  44585  exinst  44587  exinst01  44588  exinst11  44589  e2  44594  e222  44599  e233  44727  e323  44728