Theorem dfvd2ani 42173

Description: Inference form of dfvd2an 42172. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
dfvd2ani.1	⊢ (   (   𝜑   ,   𝜓   )   ▶   𝜒   )

Assertion

Ref	Expression
dfvd2ani	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Proof of Theorem dfvd2ani

Step	Hyp	Ref	Expression
1		dfvd2ani.1	. 2 ⊢ (   (   𝜑   ,   𝜓   )   ▶   𝜒   )
2		dfvd2an 42172	. 2 ⊢ ((   (   𝜑   ,   𝜓   )   ▶   𝜒   ) ↔ ((𝜑 ∧ 𝜓) → 𝜒))
3	1, 2	mpbi 229	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 396  (   wvd1 42159  (   wvhc2 42170

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 42160  df-vhc2 42171

This theorem is referenced by:  int2  42196  el021old  42291  el2122old  42309  un0.1  42369  un10  42378  un01  42379