Metamath Proof Explorer


Definition df-vd1

Description: Definition of virtual deduction. (Contributed by Alan Sare, 21-Apr-2011) (New usage is discouraged.)

Ref Expression
Assertion df-vd1 ( (    𝜑    ▶    𝜓    ) ↔ ( 𝜑 → 𝜓 ) )

Detailed syntax breakdown

Step Hyp Ref Expression
0 wph ⊢ 𝜑
1 wps ⊢ 𝜓
2 0 1 wvd1 ⊢ (    𝜑    ▶    𝜓    )
3 0 1 wi ⊢ ( 𝜑 → 𝜓 )
4 2 3 wb ⊢ ( (    𝜑    ▶    𝜓    ) ↔ ( 𝜑 → 𝜓 ) )