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Metamath Proof Explorer

Theorem dfvd2ir

Description: Right-to-left inference form of dfvd2 . (Contributed by Alan Sare, 14-Nov-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypothesis dfvd2ir.1 ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion dfvd2ir (    𝜑    ,    𝜓    ▶    𝜒    )

Proof

Step Hyp Ref Expression
1 dfvd2ir.1 ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2 dfvd2 ⊢ ( (    𝜑    ,    𝜓    ▶    𝜒    ) ↔ ( 𝜑 → ( 𝜓 → 𝜒 ) ) )
3 1 2 mpbir ⊢ (    𝜑    ,    𝜓    ▶    𝜒    )