Theorem e012

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

	Ref	Expression
Hypotheses	e012.1	⊢ 𝜑
	e012.2	⊢ (    𝜓    ▶    𝜒    )
	e012.3	⊢ (    𝜓    ,    𝜃    ▶    𝜏    )
	e012.4	⊢ ( 𝜑 → ( 𝜒 → ( 𝜏 → 𝜂 ) ) )
Assertion	e012	⊢ (    𝜓    ,    𝜃    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e012.1	⊢ 𝜑
2		e012.2	⊢ (    𝜓    ▶    𝜒    )
3		e012.3	⊢ (    𝜓    ,    𝜃    ▶    𝜏    )
4		e012.4	⊢ ( 𝜑 → ( 𝜒 → ( 𝜏 → 𝜂 ) ) )
5	1	vd01	⊢ (    𝜓    ▶    𝜑    )
6	5 2 3 4	e112	⊢ (    𝜓    ,    𝜃    ▶    𝜂    )