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Metamath Proof Explorer

Theorem e01

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 25-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e01.1 ⊢ 𝜑
e01.2 ⊢ (    𝜓    ▶    𝜒    )
e01.3 ⊢ ( 𝜑 → ( 𝜒 → 𝜃 ) )
Assertion e01 (    𝜓    ▶    𝜃    )

Proof

Step Hyp Ref Expression
1 e01.1 ⊢ 𝜑
2 e01.2 ⊢ (    𝜓    ▶    𝜒    )
3 e01.3 ⊢ ( 𝜑 → ( 𝜒 → 𝜃 ) )
4 1 vd01 ⊢ (    𝜓    ▶    𝜑    )
5 4 2 3 e11 ⊢ (    𝜓    ▶    𝜃    )