Theorem vd01 44574

Description: A virtual hypothesis virtually infers a theorem. (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
vd01.1	⊢ 𝜑

Assertion

Ref	Expression
vd01	⊢ (   𝜓   ▶   𝜑   )

Proof of Theorem vd01

Step	Hyp	Ref	Expression
1		vd01.1	. . 3 ⊢ 𝜑
2	1	a1i 11	. 2 ⊢ (𝜓 → 𝜑)
3	2	dfvd1ir 44550	1 ⊢ (   𝜓   ▶   𝜑   )

Syntax hints:  (   wvd1 44546

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 44547

This theorem is referenced by:  e210  44636  e201  44638  e021  44642  e012  44644  e102  44646  e110  44653  e101  44655  e011  44657  e100  44659  e010  44661  e001  44663  e01  44668  e10  44671  sspwimpVD  44895