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Metamath Proof Explorer

Theorem el021old

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2015) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses el021old.1 ⊢ 𝜑
el021old.2 ⊢ (    (    𝜓    ,    𝜒    )    ▶    𝜃    )
el021old.3 ⊢ ( ( 𝜑 ∧ 𝜃 ) → 𝜏 )
Assertion el021old (    (    𝜓    ,    𝜒    )    ▶    𝜏    )

Proof

Step Hyp Ref Expression
1 el021old.1 ⊢ 𝜑
2 el021old.2 ⊢ (    (    𝜓    ,    𝜒    )    ▶    𝜃    )
3 el021old.3 ⊢ ( ( 𝜑 ∧ 𝜃 ) → 𝜏 )
4 2 dfvd2ani ⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )
5 1 4 3 sylancr ⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜏 )
6 5 dfvd2anir ⊢ (    (    𝜓    ,    𝜒    )    ▶    𝜏    )