Theorem dfvd3ani 42215

Description: Inference form of dfvd3an 42214. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
dfvd3ani.1	⊢ (   (   𝜑   ,   𝜓   ,   𝜒   )   ▶   𝜃   )

Assertion

Ref	Expression
dfvd3ani	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Proof of Theorem dfvd3ani

Step	Hyp	Ref	Expression
1		dfvd3ani.1	. 2 ⊢ (   (   𝜑   ,   𝜓   ,   𝜒   )   ▶   𝜃   )
2		dfvd3an 42214	. 2 ⊢ ((   (   𝜑   ,   𝜓   ,   𝜒   )   ▶   𝜃   ) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃))
3	1, 2	mpbi 229	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1086  (   wvd1 42189  (   wvhc3 42208

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 42190  df-vhc3 42209

This theorem is referenced by:  int3  42232  el0321old  42337