Theorem vd01 42106

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 42082	1 ⊢ (   𝜓   ▶   𝜑   )

Syntax hints:  (   wvd1 42078

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 42079

This theorem is referenced by:  e210  42168  e201  42170  e021  42174  e012  42176  e102  42178  e110  42185  e101  42187  e011  42189  e100  42191  e010  42193  e001  42195  e01  42200  e10  42203  sspwimpVD  42428