Theorem e233

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 29-Feb-2012) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e233.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
	e233.2	⊢ (    𝜑    ,    𝜓    ,    𝜃    ▶    𝜏    )
	e233.3	⊢ (    𝜑    ,    𝜓    ,    𝜃    ▶    𝜂    )
	e233.4	⊢ ( 𝜒 → ( 𝜏 → ( 𝜂 → 𝜁 ) ) )
Assertion	e233	⊢ (    𝜑    ,    𝜓    ,    𝜃    ▶    𝜁    )

Proof

Step	Hyp	Ref	Expression
1		e233.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
2		e233.2	⊢ (    𝜑    ,    𝜓    ,    𝜃    ▶    𝜏    )
3		e233.3	⊢ (    𝜑    ,    𝜓    ,    𝜃    ▶    𝜂    )
4		e233.4	⊢ ( 𝜒 → ( 𝜏 → ( 𝜂 → 𝜁 ) ) )
5	1	dfvd2i	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
6	2	dfvd3i	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → 𝜏 ) ) )
7	3	dfvd3i	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → 𝜂 ) ) )
8	5 6 7 4	ee233	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → 𝜁 ) ) )
9	8	dfvd3ir	⊢ (    𝜑    ,    𝜓    ,    𝜃    ▶    𝜁    )