Theorem dfvd3an 44571

Description: Definition of a 3-hypothesis virtual deduction in vd conjunction form. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
dfvd3an	⊢ ((   (   𝜑   ,   𝜓   ,   𝜒   )   ▶   𝜃   ) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃))

Proof of Theorem dfvd3an

Step	Hyp	Ref	Expression
1		df-vd1 44547	. 2 ⊢ ((   (   𝜑   ,   𝜓   ,   𝜒   )   ▶   𝜃   ) ↔ ((   𝜑   ,   𝜓   ,   𝜒   ) → 𝜃))
2		df-vhc3 44566	. . 3 ⊢ ((   𝜑   ,   𝜓   ,   𝜒   ) ↔ (𝜑 ∧ 𝜓 ∧ 𝜒))
3	2	imbi1i 349	. 2 ⊢ (((   𝜑   ,   𝜓   ,   𝜒   ) → 𝜃) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃))
4	1, 3	bitri 275	1 ⊢ ((   (   𝜑   ,   𝜓   ,   𝜒   )   ▶   𝜃   ) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃))

Syntax hints:   → wi 4   ↔ wb 206   ∧ w3a 1086  (   wvd1 44546  (   wvhc3 44565

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 207  df-vd1 44547  df-vhc3 44566

This theorem is referenced by:  dfvd3ani  44572  dfvd3anir  44573