Metamath Proof Explorer


Theorem dfvd1ir

Description: Inference form of df-vd1 with the virtual deduction as the assertion. (Contributed by Alan Sare, 14-Nov-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypothesis dfvd1ir.1 ( 𝜑𝜓 )
Assertion dfvd1ir (    𝜑    ▶    𝜓    )

Proof

Step Hyp Ref Expression
1 dfvd1ir.1 ( 𝜑𝜓 )
2 df-vd1 ( (    𝜑    ▶    𝜓    ) ↔ ( 𝜑𝜓 ) )
3 1 2 mpbir (    𝜑    ▶    𝜓    )