Theorem e212

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

	Ref	Expression
Hypotheses	e212.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
	e212.2	⊢ (    𝜑    ▶    𝜃    )
	e212.3	⊢ (    𝜑    ,    𝜓    ▶    𝜏    )
	e212.4	⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion	e212	⊢ (    𝜑    ,    𝜓    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e212.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
2		e212.2	⊢ (    𝜑    ▶    𝜃    )
3		e212.3	⊢ (    𝜑    ,    𝜓    ▶    𝜏    )
4		e212.4	⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5	2	vd12	⊢ (    𝜑    ,    𝜓    ▶    𝜃    )
6	1 5 3 4	e222	⊢ (    𝜑    ,    𝜓    ▶    𝜂    )