Theorem dfvd3ir 45362

Description: Right-to-left inference form of dfvd3 45360. (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 45360	. 2 ⊢ ((   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   ) ↔ (𝜑 → (𝜓 → (𝜒 → 𝜃))))
3	1, 2	mpbir 234	1 ⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )

This proof depends on syntax axioms:   → wi 4  (   wvd3 45356

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105  df-vd3 45359

This theorem is used by:  vd03  45368  vd13  45370  vd23  45371  in3an  45380  idn3  45384  gen31  45390  e223  45404  e333  45501  e233  45533  e323  45534