Theorem vd01 37843

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 37810	1 ⊢ (   𝜓   ▶   𝜑   )

Syntax hints:  (   wvd1 37806

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-vd1 37807

This theorem is referenced by:  e210  37905  e201  37907  e021  37911  e012  37913  e102  37915  e110  37922  e101  37924  e011  37926  e100  37928  e010  37930  e001  37932  e01  37937  e10  37940  sspwimpVD  38177