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Metamath Proof Explorer

Theorem in3

Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 3 virtual hypotheses into an antecedent. (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypothesis in3.1 ⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
Assertion in3 (    𝜑    ,    𝜓    ▶    ( 𝜒 → 𝜃 )    )

Proof

Step Hyp Ref Expression
1 in3.1 ⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
2 1 dfvd3i ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
3 2 dfvd2ir ⊢ (    𝜑    ,    𝜓    ▶    ( 𝜒 → 𝜃 )    )