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Metamath Proof Explorer

Theorem dfvd2anir

Description: Right-to-left inference form of dfvd2an . (Contributed by Alan Sare, 23-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypothesis dfvd2anir.1 ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
Assertion dfvd2anir (    (    𝜑    ,    𝜓    )    ▶    𝜒    )

Proof

Step Hyp Ref Expression
1 dfvd2anir.1 ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
2 dfvd2an ⊢ ( (    (    𝜑    ,    𝜓    )    ▶    𝜒    ) ↔ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) )
3 1 2 mpbir ⊢ (    (    𝜑    ,    𝜓    )    ▶    𝜒    )