Theorem dfvd2anir 44162

Description: Right-to-left inference form of dfvd2an 44160. (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 44160	. 2 ⊢ ((   (   𝜑   ,   𝜓   )   ▶   𝜒   ) ↔ ((𝜑 ∧ 𝜓) → 𝜒))
3	1, 2	mpbir 230	1 ⊢ (   (   𝜑   ,   𝜓   )   ▶   𝜒   )

Syntax hints:   → wi 4   ∧ wa 394  (   wvd1 44147  (   wvhc2 44158

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 44148  df-vhc2 44159

This theorem is referenced by:  int3  44190  el021old  44279  el2122old  44297  el12  44304