Theorem dfvd2i 39118

Description: Inference form of dfvd2 39112. (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 39112	. 2 ⊢ ((   𝜑   ,   𝜓   ▶   𝜒   ) ↔ (𝜑 → (𝜓 → 𝜒)))
3	1, 2	mpbi 220	1 ⊢ (𝜑 → (𝜓 → 𝜒))

Syntax hints:   → wi 4  (   wvd2 39110

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 197  df-an 385  df-vd2 39111

This theorem is referenced by:  vd23  39144  in2  39147  in2an  39150  gen21  39161  gen21nv  39162  gen22  39164  exinst  39166  exinst01  39167  exinst11  39168  e2  39173  e222  39178  e233  39309  e323  39310