Theorem vd01 44587

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 44563	1 ⊢ (   𝜓   ▶   𝜑   )

Syntax hints:  (   wvd1 44559

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 207  df-vd1 44560

This theorem is referenced by:  e210  44649  e201  44651  e021  44655  e012  44657  e102  44659  e110  44666  e101  44668  e011  44670  e100  44672  e010  44674  e001  44676  e01  44681  e10  44684  sspwimpVD  44908