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    )