Theorem e30an

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

	Ref	Expression
Hypotheses	e30an.1	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
	e30an.2	⊢ 𝜏
	e30an.3	⊢ ( ( 𝜃 ∧ 𝜏 ) → 𝜂 )
Assertion	e30an	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e30an.1	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
2		e30an.2	⊢ 𝜏
3		e30an.3	⊢ ( ( 𝜃 ∧ 𝜏 ) → 𝜂 )
4	3	ex	⊢ ( 𝜃 → ( 𝜏 → 𝜂 ) )
5	1 2 4	e30	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜂    )