Theorem dfvd1ir 44571

Description: Inference form of df-vd1 44568 with the virtual deduction as the assertion. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
dfvd1ir.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
dfvd1ir	⊢ (   𝜑   ▶   𝜓   )

Proof of Theorem dfvd1ir

Step	Hyp	Ref	Expression
1		dfvd1ir.1	. 2 ⊢ (𝜑 → 𝜓)
2		df-vd1 44568	. 2 ⊢ ((   𝜑   ▶   𝜓   ) ↔ (𝜑 → 𝜓))
3	1, 2	mpbir 231	1 ⊢ (   𝜑   ▶   𝜓   )

Syntax hints:   → wi 4  (   wvd1 44567

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 207  df-vd1 44568

This theorem is referenced by:  idn1  44572  vd01  44595  in2  44603  int2  44604  gen11nv  44615  gen12  44616  exinst01  44623  exinst11  44624  e1a  44625  el1  44626  e111  44672  e1111  44673  un0.1  44777  un10  44786  un01  44787  sbcoreleleqVD  44857  2uasbanhVD  44909