Theorem dfvd2 45561

Description: Definition of a 2-hypothesis virtual deduction. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
dfvd2	⊢ ((   𝜑   ,   𝜓   ▶   𝜒   ) ↔ (𝜑 → (𝜓 → 𝜒)))

Proof of Theorem dfvd2

Step	Hyp	Ref	Expression
1		df-vd2 45560	. 2 ⊢ ((   𝜑   ,   𝜓   ▶   𝜒   ) ↔ ((𝜑 ∧ 𝜓) → 𝜒))
2		impexp 456	. 2 ⊢ (((𝜑 ∧ 𝜓) → 𝜒) ↔ (𝜑 → (𝜓 → 𝜒)))
3	1, 2	bitri 278	1 ⊢ ((   𝜑   ,   𝜓   ▶   𝜒   ) ↔ (𝜑 → (𝜓 → 𝜒)))

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∧ wa 401  (   wvd2 45559

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-an 402  df-vd2 45560

This theorem is used by:  dfvd2i  45567  dfvd2ir  45568  dfvd2imp  45585  dfvd2impr  45586