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Metamath Proof Explorer

Theorem e100

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

Ref Expression
Hypotheses e100.1 ⊢ (    𝜑    ▶    𝜓    )
e100.2 ⊢ 𝜒
e100.3 ⊢ 𝜃
e100.4 ⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
Assertion e100 (    𝜑    ▶    𝜏    )

Proof

Step Hyp Ref Expression
1 e100.1 ⊢ (    𝜑    ▶    𝜓    )
2 e100.2 ⊢ 𝜒
3 e100.3 ⊢ 𝜃
4 e100.4 ⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
5 2 vd01 ⊢ (    𝜑    ▶    𝜒    )
6 3 vd01 ⊢ (    𝜑    ▶    𝜃    )
7 1 5 6 4 e111 ⊢ (    𝜑    ▶    𝜏    )