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Metamath Proof Explorer

Theorem e002

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

Ref Expression
Hypotheses e002.1 ⊢ 𝜑
e002.2 ⊢ 𝜓
e002.3 ⊢ (    𝜒    ,    𝜃    ▶    𝜏    )
e002.4 ⊢ ( 𝜑 → ( 𝜓 → ( 𝜏 → 𝜂 ) ) )
Assertion e002 (    𝜒    ,    𝜃    ▶    𝜂    )

Proof

Step Hyp Ref Expression
1 e002.1 ⊢ 𝜑
2 e002.2 ⊢ 𝜓
3 e002.3 ⊢ (    𝜒    ,    𝜃    ▶    𝜏    )
4 e002.4 ⊢ ( 𝜑 → ( 𝜓 → ( 𝜏 → 𝜂 ) ) )
5 1 vd02 ⊢ (    𝜒    ,    𝜃    ▶    𝜑    )
6 2 vd02 ⊢ (    𝜒    ,    𝜃    ▶    𝜓    )
7 5 6 3 4 e222 ⊢ (    𝜒    ,    𝜃    ▶    𝜂    )