Theorem dfvd3i 42212

Description: Inference form of dfvd3 42211. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
dfvd3i.1	⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )

Assertion

Ref	Expression
dfvd3i	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))

Proof of Theorem dfvd3i

Step	Hyp	Ref	Expression
1		dfvd3i.1	. 2 ⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
2		dfvd3 42211	. 2 ⊢ ((   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   ) ↔ (𝜑 → (𝜓 → (𝜒 → 𝜃))))
3	1, 2	mpbi 229	1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))

Syntax hints:   → wi 4  (   wvd3 42207

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 206  df-an 397  df-3an 1088  df-vd3 42210

This theorem is referenced by:  in3  42229  in3an  42231  gen31  42241  e333  42353  e233  42385  e323  42386