Theorem vd01 40347

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 40323	1 ⊢ (   𝜓   ▶   𝜑   )

Syntax hints:  (   wvd1 40319

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 199  df-vd1 40320

This theorem is referenced by:  e210  40409  e201  40411  e021  40415  e012  40417  e102  40419  e110  40426  e101  40428  e011  40430  e100  40432  e010  40434  e001  40436  e01  40441  e10  40444  sspwimpVD  40669