Theorem e31an

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

	Ref	Expression
Hypotheses	e31an.1	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
	e31an.2	⊢ (    𝜑    ▶    𝜏    )
	e31an.3	⊢ ( ( 𝜃 ∧ 𝜏 ) → 𝜂 )
Assertion	e31an	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e31an.1	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
2		e31an.2	⊢ (    𝜑    ▶    𝜏    )
3		e31an.3	⊢ ( ( 𝜃 ∧ 𝜏 ) → 𝜂 )
4	3	ex	⊢ ( 𝜃 → ( 𝜏 → 𝜂 ) )
5	1 2 4	e31	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜂    )