Theorem dfvd2i 45409

Description: Inference form of dfvd2 45403. (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 45403	. 2 ⊢ ((   𝜑   ,   𝜓   ▶   𝜒   ) ↔ (𝜑 → (𝜓 → 𝜒)))
3	1, 2	mpbi 233	1 ⊢ (𝜑 → (𝜓 → 𝜒))

This proof depends on syntax axioms:   → wi 4  (   wvd2 45401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-vd2 45402

This theorem is used by:  vd23  45426  in2  45429  in2an  45432  gen21  45443  gen21nv  45444  gen22  45446  exinst  45448  exinst01  45449  exinst11  45450  e2  45455  e222  45460  e233  45588  e323  45589