Theorem dfvd3anir 45365

Description: Right-to-left inference form of dfvd3an 45363. (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 45363	. 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   ∧ w3a 1103  (   wvd1 45338  (   wvhc3 45357

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-vd1 45339  df-vhc3 45358

This theorem is used by:  el0321old  45485  el123  45532