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    )