Theorem e02

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 14-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e02.1	⊢ 𝜑
	e02.2	⊢ (    𝜓    ,    𝜒    ▶    𝜃    )
	e02.3	⊢ ( 𝜑 → ( 𝜃 → 𝜏 ) )
Assertion	e02	⊢ (    𝜓    ,    𝜒    ▶    𝜏    )

Proof

Step	Hyp	Ref	Expression
1		e02.1	⊢ 𝜑
2		e02.2	⊢ (    𝜓    ,    𝜒    ▶    𝜃    )
3		e02.3	⊢ ( 𝜑 → ( 𝜃 → 𝜏 ) )
4	1	vd02	⊢ (    𝜓    ,    𝜒    ▶    𝜑    )
5	4 2 3	e22	⊢ (    𝜓    ,    𝜒    ▶    𝜏    )