Theorem dfvd2ir 45323

Description: Right-to-left inference form of dfvd2 45316. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
dfvd2ir.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
dfvd2ir	⊢ (   𝜑   ,   𝜓   ▶   𝜒   )

Proof of Theorem dfvd2ir

Step	Hyp	Ref	Expression
1		dfvd2ir.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		dfvd2 45316	. 2 ⊢ ((   𝜑   ,   𝜓   ▶   𝜒   ) ↔ (𝜑 → (𝜓 → 𝜒)))
3	1, 2	mpbir 234	1 ⊢ (   𝜑   ,   𝜓   ▶   𝜒   )

This proof depends on syntax axioms:   → wi 4  (   wvd2 45314

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 401  df-vd2 45315

This theorem is used by:  vd02  45335  vd12  45337  in2an  45345  in3  45346  idn2  45350  gen21  45356  gen21nv  45357  gen22  45359  e2  45368  e222  45373