Theorem e211

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

	Ref	Expression
Hypotheses	e211.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
	e211.2	⊢ (    𝜑    ▶    𝜃    )
	e211.3	⊢ (    𝜑    ▶    𝜏    )
	e211.4	⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion	e211	⊢ (    𝜑    ,    𝜓    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e211.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
2		e211.2	⊢ (    𝜑    ▶    𝜃    )
3		e211.3	⊢ (    𝜑    ▶    𝜏    )
4		e211.4	⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5	2	vd12	⊢ (    𝜑    ,    𝜓    ▶    𝜃    )
6	3	vd12	⊢ (    𝜑    ,    𝜓    ▶    𝜏    )
7	1 5 6 4	e222	⊢ (    𝜑    ,    𝜓    ▶    𝜂    )