Theorem vd01 45565

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 45541	1 ⊢ (   𝜓   ▶   𝜑   )

This proof depends on syntax axioms:  (   wvd1 45537

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-vd1 45538

This theorem is used by:  e210  45627  e201  45629  e021  45633  e012  45635  e102  45637  e110  45644  e101  45646  e011  45648  e100  45650  e010  45652  e001  45654  e01  45659  e10  45662  sspwimpVD  45886