Theorem dfvd2an 45349

Description: Definition of a 2-hypothesis virtual deduction in vd conjunction form. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
dfvd2an	⊢ ((   (   𝜑   ,   𝜓   )   ▶   𝜒   ) ↔ ((𝜑 ∧ 𝜓) → 𝜒))

Proof of Theorem dfvd2an

Step	Hyp	Ref	Expression
1		df-vd1 45337	. 2 ⊢ ((   (   𝜑   ,   𝜓   )   ▶   𝜒   ) ↔ ((   𝜑   ,   𝜓   ) → 𝜒))
2		df-vhc2 45348	. . 3 ⊢ ((   𝜑   ,   𝜓   ) ↔ (𝜑 ∧ 𝜓))
3	2	imbi1i 352	. 2 ⊢ (((   𝜑   ,   𝜓   ) → 𝜒) ↔ ((𝜑 ∧ 𝜓) → 𝜒))
4	1, 3	bitri 278	1 ⊢ ((   (   𝜑   ,   𝜓   )   ▶   𝜒   ) ↔ ((𝜑 ∧ 𝜓) → 𝜒))

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∧ wa 401  (   wvd1 45336  (   wvhc2 45347

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 45337  df-vhc2 45348

This theorem is used by:  dfvd2ani  45350  dfvd2anir  45351  iden2  45381