Theorem dfvd3ir 42523

Description: Right-to-left inference form of dfvd3 42521. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
dfvd3ir.1	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))

Assertion

Ref	Expression
dfvd3ir	⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )

Proof of Theorem dfvd3ir

Step	Hyp	Ref	Expression
1		dfvd3ir.1	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
2		dfvd3 42521	. 2 ⊢ ((   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   ) ↔ (𝜑 → (𝜓 → (𝜒 → 𝜃))))
3	1, 2	mpbir 230	1 ⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )

Syntax hints:   → wi 4  (   wvd3 42517

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 42520

This theorem is referenced by:  vd03  42529  vd13  42531  vd23  42532  in3an  42541  idn3  42545  gen31  42551  e223  42565  e333  42663  e233  42695  e323  42696