Theorem e30

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

	Ref	Expression
Hypotheses	e30.1	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
	e30.2	⊢ 𝜏
	e30.3	⊢ ( 𝜃 → ( 𝜏 → 𝜂 ) )
Assertion	e30	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e30.1	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
2		e30.2	⊢ 𝜏
3		e30.3	⊢ ( 𝜃 → ( 𝜏 → 𝜂 ) )
4	2	vd03	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜏    )
5	1 4 3	e33	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜂    )