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Metamath Proof Explorer

Theorem e020

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e020.1 ⊢ 𝜑
e020.2 ⊢ (    𝜓    ,    𝜒    ▶    𝜃    )
e020.3 ⊢ 𝜏
e020.4 ⊢ ( 𝜑 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion e020 (    𝜓    ,    𝜒    ▶    𝜂    )

Proof

Step Hyp Ref Expression
1 e020.1 ⊢ 𝜑
2 e020.2 ⊢ (    𝜓    ,    𝜒    ▶    𝜃    )
3 e020.3 ⊢ 𝜏
4 e020.4 ⊢ ( 𝜑 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5 1 vd02 ⊢ (    𝜓    ,    𝜒    ▶    𝜑    )
6 3 vd02 ⊢ (    𝜓    ,    𝜒    ▶    𝜏    )
7 5 2 6 4 e222 ⊢ (    𝜓    ,    𝜒    ▶    𝜂    )