Theorem e120

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 10-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e120.1	⊢ (    𝜑    ▶    𝜓    )
	e120.2	⊢ (    𝜑    ,    𝜒    ▶    𝜃    )
	e120.3	⊢ 𝜏
	e120.4	⊢ ( 𝜓 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion	e120	⊢ (    𝜑    ,    𝜒    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e120.1	⊢ (    𝜑    ▶    𝜓    )
2		e120.2	⊢ (    𝜑    ,    𝜒    ▶    𝜃    )
3		e120.3	⊢ 𝜏
4		e120.4	⊢ ( 𝜓 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5	1	vd12	⊢ (    𝜑    ,    𝜒    ▶    𝜓    )
6	5 2 3 4	e220	⊢ (    𝜑    ,    𝜒    ▶    𝜂    )