Theorem e31

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

	Ref	Expression
Hypotheses	e31.1	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
	e31.2	⊢ (    𝜑    ▶    𝜏    )
	e31.3	⊢ ( 𝜃 → ( 𝜏 → 𝜂 ) )
Assertion	e31	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e31.1	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
2		e31.2	⊢ (    𝜑    ▶    𝜏    )
3		e31.3	⊢ ( 𝜃 → ( 𝜏 → 𝜂 ) )
4	2	vd13	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜏    )
5	1 4 3	e33	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜂    )