Theorem e23

Description: A virtual deduction elimination rule (see syl10 ). (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e23.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
	e23.2	⊢ (    𝜑    ,    𝜓    ,    𝜃    ▶    𝜏    )
	e23.3	⊢ ( 𝜒 → ( 𝜏 → 𝜂 ) )
Assertion	e23	⊢ (    𝜑    ,    𝜓    ,    𝜃    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e23.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
2		e23.2	⊢ (    𝜑    ,    𝜓    ,    𝜃    ▶    𝜏    )
3		e23.3	⊢ ( 𝜒 → ( 𝜏 → 𝜂 ) )
4	1	vd23	⊢ (    𝜑    ,    𝜓    ,    𝜃    ▶    𝜒    )
5	4 2 3	e33	⊢ (    𝜑    ,    𝜓    ,    𝜃    ▶    𝜂    )