Theorem dfvd3ir 39637

Description: Right-to-left inference form of dfvd3 39635. (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 39635	. 2 ⊢ ((   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   ) ↔ (𝜑 → (𝜓 → (𝜒 → 𝜃))))
3	1, 2	mpbir 223	1 ⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )

Syntax hints:   → wi 4  (   wvd3 39631

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 199  df-an 387  df-3an 1115  df-vd3 39634

This theorem is referenced by:  vd03  39652  vd13  39654  vd23  39655  in3an  39664  idn3  39668  gen31  39674  e223  39688  e333  39787  e233  39819  e323  39820