Theorem vd01 38822

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 38789	1 ⊢ (   𝜓   ▶   𝜑   )

Syntax hints:  (   wvd1 38785

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 197  df-vd1 38786

This theorem is referenced by:  e210  38884  e201  38886  e021  38890  e012  38892  e102  38894  e110  38901  e101  38903  e011  38905  e100  38907  e010  38909  e001  38911  e01  38916  e10  38919  sspwimpVD  39155