Theorem dfvd3anir 42105

Description: Right-to-left inference form of dfvd3an 42103. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
dfvd3anir.1	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Assertion

Ref	Expression
dfvd3anir	⊢ (   (   𝜑   ,   𝜓   ,   𝜒   )   ▶   𝜃   )

Proof of Theorem dfvd3anir

Step	Hyp	Ref	Expression
1		dfvd3anir.1	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)
2		dfvd3an 42103	. 2 ⊢ ((   (   𝜑   ,   𝜓   ,   𝜒   )   ▶   𝜃   ) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃))
3	1, 2	mpbir 230	1 ⊢ (   (   𝜑   ,   𝜓   ,   𝜒   )   ▶   𝜃   )

Syntax hints:   → wi 4   ∧ w3a 1085  (   wvd1 42078  (   wvhc3 42097

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-vd1 42079  df-vhc3 42098

This theorem is referenced by:  el0321old  42226  el123  42273