Theorem e101

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

	Ref	Expression
Hypotheses	e101.1	⊢ (    𝜑    ▶    𝜓    )
	e101.2	⊢ 𝜒
	e101.3	⊢ (    𝜑    ▶    𝜃    )
	e101.4	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
Assertion	e101	⊢ (    𝜑    ▶    𝜏    )

Proof

Step	Hyp	Ref	Expression
1		e101.1	⊢ (    𝜑    ▶    𝜓    )
2		e101.2	⊢ 𝜒
3		e101.3	⊢ (    𝜑    ▶    𝜃    )
4		e101.4	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
5	2	vd01	⊢ (    𝜑    ▶    𝜒    )
6	1 5 3 4	e111	⊢ (    𝜑    ▶    𝜏    )