Theorem vd01 45024

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 45000	1 ⊢ (   𝜓   ▶   𝜑   )

Syntax hints:  (   wvd1 44996

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 44997

This theorem is referenced by:  e210  45086  e201  45088  e021  45092  e012  45094  e102  45096  e110  45103  e101  45105  e011  45107  e100  45109  e010  45111  e001  45113  e01  45118  e10  45121  sspwimpVD  45345