Theorem dfvd2imp 45372

Description: The virtual deduction form of a 2-antecedent nested implication implies the 2-antecedent nested implication. (Contributed by Alan Sare, 21-Apr-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
dfvd2imp	⊢ ((   𝜑   ,   𝜓   ▶   𝜒   ) → (𝜑 → (𝜓 → 𝜒)))

Proof of Theorem dfvd2imp

Step	Hyp	Ref	Expression
1		dfvd2 45348	. 2 ⊢ ((   𝜑   ,   𝜓   ▶   𝜒   ) ↔ (𝜑 → (𝜓 → 𝜒)))
2	1	biimpi 219	1 ⊢ ((   𝜑   ,   𝜓   ▶   𝜒   ) → (𝜑 → (𝜓 → 𝜒)))

This proof depends on syntax axioms:   → wi 4  (   wvd2 45346

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 45347

This theorem is used by: (None)