Theorem vd01 43129

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 43105	1 ⊢ (   𝜓   ▶   𝜑   )

Syntax hints:  (   wvd1 43101

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 206  df-vd1 43102

This theorem is referenced by:  e210  43191  e201  43193  e021  43197  e012  43199  e102  43201  e110  43208  e101  43210  e011  43212  e100  43214  e010  43216  e001  43218  e01  43223  e10  43226  sspwimpVD  43451