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Metamath Proof Explorer

Theorem el0321old

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

Ref Expression
Hypotheses el0321old.1 ⊢ 𝜑
el0321old.2 ⊢ (    (    𝜓    ,    𝜒    ,    𝜃    )    ▶    𝜏    )
el0321old.3 ⊢ ( ( 𝜑 ∧ 𝜏 ) → 𝜂 )
Assertion el0321old (    (    𝜓    ,    𝜒    ,    𝜃    )    ▶    𝜂    )

Proof

Step Hyp Ref Expression
1 el0321old.1 ⊢ 𝜑
2 el0321old.2 ⊢ (    (    𝜓    ,    𝜒    ,    𝜃    )    ▶    𝜏    )
3 el0321old.3 ⊢ ( ( 𝜑 ∧ 𝜏 ) → 𝜂 )
4 2 dfvd3ani ⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜏 )
5 1 4 3 eel0321old ⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜂 )
6 5 dfvd3anir ⊢ (    (    𝜓    ,    𝜒    ,    𝜃    )    ▶    𝜂    )