Theorem e03

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e03.1	⊢ 𝜑
	e03.2	⊢ (    𝜓    ,    𝜒    ,    𝜃    ▶    𝜏    )
	e03.3	⊢ ( 𝜑 → ( 𝜏 → 𝜂 ) )
Assertion	e03	⊢ (    𝜓    ,    𝜒    ,    𝜃    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e03.1	⊢ 𝜑
2		e03.2	⊢ (    𝜓    ,    𝜒    ,    𝜃    ▶    𝜏    )
3		e03.3	⊢ ( 𝜑 → ( 𝜏 → 𝜂 ) )
4	1	vd03	⊢ (    𝜓    ,    𝜒    ,    𝜃    ▶    𝜑    )
5	4 2 3	e33	⊢ (    𝜓    ,    𝜒    ,    𝜃    ▶    𝜂    )