Theorem e011

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

	Ref	Expression
Hypotheses	e011.1	⊢ 𝜑
	e011.2	⊢ (    𝜓    ▶    𝜒    )
	e011.3	⊢ (    𝜓    ▶    𝜃    )
	e011.4	⊢ ( 𝜑 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
Assertion	e011	⊢ (    𝜓    ▶    𝜏    )

Proof

Step	Hyp	Ref	Expression
1		e011.1	⊢ 𝜑
2		e011.2	⊢ (    𝜓    ▶    𝜒    )
3		e011.3	⊢ (    𝜓    ▶    𝜃    )
4		e011.4	⊢ ( 𝜑 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
5	1	vd01	⊢ (    𝜓    ▶    𝜑    )
6	5 2 3 4	e111	⊢ (    𝜓    ▶    𝜏    )