Theorem dfvd3i 40919

Description: Inference form of dfvd3 40918. (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 40918	. 2 ⊢ ((   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   ) ↔ (𝜑 → (𝜓 → (𝜒 → 𝜃))))
3	1, 2	mpbi 232	1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))

Syntax hints:   → wi 4  (   wvd3 40914

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-3an 1085  df-vd3 40917

This theorem is referenced by:  in3  40936  in3an  40938  gen31  40948  e333  41060  e233  41092  e323  41093