Theorem dfvd2anir 45353

Description: Right-to-left inference form of dfvd2an 45351. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
dfvd2anir.1	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Assertion

Ref	Expression
dfvd2anir	⊢ (   (   𝜑   ,   𝜓   )   ▶   𝜒   )

Proof of Theorem dfvd2anir

Step	Hyp	Ref	Expression
1		dfvd2anir.1	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)
2		dfvd2an 45351	. 2 ⊢ ((   (   𝜑   ,   𝜓   )   ▶   𝜒   ) ↔ ((𝜑 ∧ 𝜓) → 𝜒))
3	1, 2	mpbir 234	1 ⊢ (   (   𝜑   ,   𝜓   )   ▶   𝜒   )

This proof depends on syntax axioms:   → wi 4   ∧ wa 401  (   wvd1 45338  (   wvhc2 45349

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-vhc2 45350

This theorem is used by:  int3  45381  el021old  45470  el2122old  45487  el12  45494