Theorem e002

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

	Ref	Expression
Hypotheses	e002.1	⊢ 𝜑
	e002.2	⊢ 𝜓
	e002.3	⊢ (    𝜒    ,    𝜃    ▶    𝜏    )
	e002.4	⊢ ( 𝜑 → ( 𝜓 → ( 𝜏 → 𝜂 ) ) )
Assertion	e002	⊢ (    𝜒    ,    𝜃    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e002.1	⊢ 𝜑
2		e002.2	⊢ 𝜓
3		e002.3	⊢ (    𝜒    ,    𝜃    ▶    𝜏    )
4		e002.4	⊢ ( 𝜑 → ( 𝜓 → ( 𝜏 → 𝜂 ) ) )
5	1	vd02	⊢ (    𝜒    ,    𝜃    ▶    𝜑    )
6	2	vd02	⊢ (    𝜒    ,    𝜃    ▶    𝜓    )
7	5 6 3 4	e222	⊢ (    𝜒    ,    𝜃    ▶    𝜂    )