Theorem e202

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

	Ref	Expression
Hypotheses	e202.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
	e202.2	⊢ 𝜃
	e202.3	⊢ (    𝜑    ,    𝜓    ▶    𝜏    )
	e202.4	⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion	e202	⊢ (    𝜑    ,    𝜓    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e202.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
2		e202.2	⊢ 𝜃
3		e202.3	⊢ (    𝜑    ,    𝜓    ▶    𝜏    )
4		e202.4	⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5	2	vd02	⊢ (    𝜑    ,    𝜓    ▶    𝜃    )
6	1 5 3 4	e222	⊢ (    𝜑    ,    𝜓    ▶    𝜂    )