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Metamath Proof Explorer

Theorem e010

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

Ref Expression
Hypotheses e010.1 ⊢ 𝜑
e010.2 ⊢ (    𝜓    ▶    𝜒    )
e010.3 ⊢ 𝜃
e010.4 ⊢ ( 𝜑 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
Assertion e010 (    𝜓    ▶    𝜏    )

Proof

Step Hyp Ref Expression
1 e010.1 ⊢ 𝜑
2 e010.2 ⊢ (    𝜓    ▶    𝜒    )
3 e010.3 ⊢ 𝜃
4 e010.4 ⊢ ( 𝜑 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
5 1 vd01 ⊢ (    𝜓    ▶    𝜑    )
6 3 vd01 ⊢ (    𝜓    ▶    𝜃    )
7 5 2 6 4 e111 ⊢ (    𝜓    ▶    𝜏    )