Theorem e102

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

	Ref	Expression
Hypotheses	e102.1	⊢ (    𝜑    ▶    𝜓    )
	e102.2	⊢ 𝜒
	e102.3	⊢ (    𝜑    ,    𝜃    ▶    𝜏    )
	e102.4	⊢ ( 𝜓 → ( 𝜒 → ( 𝜏 → 𝜂 ) ) )
Assertion	e102	⊢ (    𝜑    ,    𝜃    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e102.1	⊢ (    𝜑    ▶    𝜓    )
2		e102.2	⊢ 𝜒
3		e102.3	⊢ (    𝜑    ,    𝜃    ▶    𝜏    )
4		e102.4	⊢ ( 𝜓 → ( 𝜒 → ( 𝜏 → 𝜂 ) ) )
5	2	vd01	⊢ (    𝜑    ▶    𝜒    )
6	1 5 3 4	e112	⊢ (    𝜑    ,    𝜃    ▶    𝜂    )