Theorem vd01 45420

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 45396	1 ⊢ (   𝜓   ▶   𝜑   )

This proof depends on syntax axioms:  (   wvd1 45392

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-vd1 45393

This theorem is used by:  e210  45482  e201  45484  e021  45488  e012  45490  e102  45492  e110  45499  e101  45501  e011  45503  e100  45505  e010  45507  e001  45509  e01  45514  e10  45517  sspwimpVD  45741