Theorem e112

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

	Ref	Expression
Hypotheses	e112.1	⊢ (    𝜑    ▶    𝜓    )
	e112.2	⊢ (    𝜑    ▶    𝜒    )
	e112.3	⊢ (    𝜑    ,    𝜃    ▶    𝜏    )
	e112.4	⊢ ( 𝜓 → ( 𝜒 → ( 𝜏 → 𝜂 ) ) )
Assertion	e112	⊢ (    𝜑    ,    𝜃    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e112.1	⊢ (    𝜑    ▶    𝜓    )
2		e112.2	⊢ (    𝜑    ▶    𝜒    )
3		e112.3	⊢ (    𝜑    ,    𝜃    ▶    𝜏    )
4		e112.4	⊢ ( 𝜓 → ( 𝜒 → ( 𝜏 → 𝜂 ) ) )
5	1	vd12	⊢ (    𝜑    ,    𝜃    ▶    𝜓    )
6	2	vd12	⊢ (    𝜑    ,    𝜃    ▶    𝜒    )
7	5 6 3 4	e222	⊢ (    𝜑    ,    𝜃    ▶    𝜂    )