Theorem vd01 44559

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 44535	1 ⊢ (   𝜓   ▶   𝜑   )

Syntax hints:  (   wvd1 44531

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 44532

This theorem is referenced by:  e210  44621  e201  44623  e021  44627  e012  44629  e102  44631  e110  44638  e101  44640  e011  44642  e100  44644  e010  44646  e001  44648  e01  44653  e10  44656  sspwimpVD  44880