Theorem vd01 40924

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 40900	1 ⊢ (   𝜓   ▶   𝜑   )

Syntax hints:  (   wvd1 40896

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 209  df-vd1 40897

This theorem is referenced by:  e210  40986  e201  40988  e021  40992  e012  40994  e102  40996  e110  41003  e101  41005  e011  41007  e100  41009  e010  41011  e001  41013  e01  41018  e10  41021  sspwimpVD  41246