Theorem e020

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

	Ref	Expression
Hypotheses	e020.1	⊢ 𝜑
	e020.2	⊢ (    𝜓    ,    𝜒    ▶    𝜃    )
	e020.3	⊢ 𝜏
	e020.4	⊢ ( 𝜑 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion	e020	⊢ (    𝜓    ,    𝜒    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e020.1	⊢ 𝜑
2		e020.2	⊢ (    𝜓    ,    𝜒    ▶    𝜃    )
3		e020.3	⊢ 𝜏
4		e020.4	⊢ ( 𝜑 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5	1	vd02	⊢ (    𝜓    ,    𝜒    ▶    𝜑    )
6	3	vd02	⊢ (    𝜓    ,    𝜒    ▶    𝜏    )
7	5 2 6 4	e222	⊢ (    𝜓    ,    𝜒    ▶    𝜂    )