Theorem e110

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

	Ref	Expression
Hypotheses	e110.1	⊢ (    𝜑    ▶    𝜓    )
	e110.2	⊢ (    𝜑    ▶    𝜒    )
	e110.3	⊢ 𝜃
	e110.4	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
Assertion	e110	⊢ (    𝜑    ▶    𝜏    )

Proof

Step	Hyp	Ref	Expression
1		e110.1	⊢ (    𝜑    ▶    𝜓    )
2		e110.2	⊢ (    𝜑    ▶    𝜒    )
3		e110.3	⊢ 𝜃
4		e110.4	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
5	3	vd01	⊢ (    𝜑    ▶    𝜃    )
6	1 2 5 4	e111	⊢ (    𝜑    ▶    𝜏    )