Theorem vd01 45191

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 45167	1 ⊢ (   𝜓   ▶   𝜑   )

Syntax hints:  (   wvd1 45163

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 210  df-vd1 45164

This theorem is referenced by:  e210  45253  e201  45255  e021  45259  e012  45261  e102  45263  e110  45270  e101  45272  e011  45274  e100  45276  e010  45278  e001  45280  e01  45285  e10  45288  sspwimpVD  45512