Theorem dfvd2impr 45354

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

Assertion

Ref	Expression
dfvd2impr	⊢ ((𝜑 → (𝜓 → 𝜒)) → (   𝜑   ,   𝜓   ▶   𝜒   ))

Proof of Theorem dfvd2impr

Step	Hyp	Ref	Expression
1		dfvd2 45329	. 2 ⊢ ((   𝜑   ,   𝜓   ▶   𝜒   ) ↔ (𝜑 → (𝜓 → 𝜒)))
2	1	biimpri 231	1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (   𝜑   ,   𝜓   ▶   𝜒   ))

This proof depends on syntax axioms:   → wi 4  (   wvd2 45327

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 45328

This theorem is used by: (None)