Theorem dfvd3i 44563

Description: Inference form of dfvd3 44562. (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 44562	. 2 ⊢ ((   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   ) ↔ (𝜑 → (𝜓 → (𝜒 → 𝜃))))
3	1, 2	mpbi 230	1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))

Syntax hints:   → wi 4  (   wvd3 44558

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-3an 1089  df-vd3 44561

This theorem is referenced by:  in3  44580  in3an  44582  gen31  44592  e333  44704  e233  44736  e323  44737