Theorem vd01 44950

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 44926	1 ⊢ (   𝜓   ▶   𝜑   )

Syntax hints:  (   wvd1 44922

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 44923

This theorem is referenced by:  e210  45012  e201  45014  e021  45018  e012  45020  e102  45022  e110  45029  e101  45031  e011  45033  e100  45035  e010  45037  e001  45039  e01  45044  e10  45047  sspwimpVD  45271