Theorem vd01 42217

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 42193	1 ⊢ (   𝜓   ▶   𝜑   )

Syntax hints:  (   wvd1 42189

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 42190

This theorem is referenced by:  e210  42279  e201  42281  e021  42285  e012  42287  e102  42289  e110  42296  e101  42298  e011  42300  e100  42302  e010  42304  e001  42306  e01  42311  e10  42314  sspwimpVD  42539