Theorem e13

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e13.1	⊢ (    𝜑    ▶    𝜓    )
	e13.2	⊢ (    𝜑    ,    𝜒    ,    𝜃    ▶    𝜏    )
	e13.3	⊢ ( 𝜓 → ( 𝜏 → 𝜂 ) )
Assertion	e13	⊢ (    𝜑    ,    𝜒    ,    𝜃    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e13.1	⊢ (    𝜑    ▶    𝜓    )
2		e13.2	⊢ (    𝜑    ,    𝜒    ,    𝜃    ▶    𝜏    )
3		e13.3	⊢ ( 𝜓 → ( 𝜏 → 𝜂 ) )
4	1	vd13	⊢ (    𝜑    ,    𝜒    ,    𝜃    ▶    𝜓    )
5	4 2 3	e33	⊢ (    𝜑    ,    𝜒    ,    𝜃    ▶    𝜂    )