Theorem dfvd2ir 37823

Description: Right-to-left inference form of dfvd2 37816. (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 37816	. 2 ⊢ ((   𝜑   ,   𝜓   ▶   𝜒   ) ↔ (𝜑 → (𝜓 → 𝜒)))
3	1, 2	mpbir 220	1 ⊢ (   𝜑   ,   𝜓   ▶   𝜒   )

Syntax hints:   → wi 4  (   wvd2 37814

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 196  df-an 385  df-vd2 37815

This theorem is referenced by:  vd02  37844  vd12  37846  in2an  37854  in3  37855  idn2  37859  gen21  37865  gen21nv  37866  gen22  37868  e2  37877  e222  37882