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Metamath Proof Explorer

Theorem e001

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

Ref Expression
Hypotheses e001.1 ⊢ 𝜑
e001.2 ⊢ 𝜓
e001.3 ⊢ (    𝜒    ▶    𝜃    )
e001.4 ⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → 𝜏 ) ) )
Assertion e001 (    𝜒    ▶    𝜏    )

Proof

Step Hyp Ref Expression
1 e001.1 ⊢ 𝜑
2 e001.2 ⊢ 𝜓
3 e001.3 ⊢ (    𝜒    ▶    𝜃    )
4 e001.4 ⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → 𝜏 ) ) )
5 1 vd01 ⊢ (    𝜒    ▶    𝜑    )
6 2 vd01 ⊢ (    𝜒    ▶    𝜓    )
7 5 6 3 4 e111 ⊢ (    𝜒    ▶    𝜏    )