Theorem dfvd2i 40939

Description: Inference form of dfvd2 40933. (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 40933	. 2 ⊢ ((   𝜑   ,   𝜓   ▶   𝜒   ) ↔ (𝜑 → (𝜓 → 𝜒)))
3	1, 2	mpbi 232	1 ⊢ (𝜑 → (𝜓 → 𝜒))

Syntax hints:   → wi 4  (   wvd2 40931

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 399  df-vd2 40932

This theorem is referenced by:  vd23  40956  in2  40959  in2an  40962  gen21  40973  gen21nv  40974  gen22  40976  exinst  40978  exinst01  40979  exinst11  40980  e2  40985  e222  40990  e233  41119  e323  41120