Theorem e01

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 25-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e01.1	⊢ 𝜑
	e01.2	⊢ (    𝜓    ▶    𝜒    )
	e01.3	⊢ ( 𝜑 → ( 𝜒 → 𝜃 ) )
Assertion	e01	⊢ (    𝜓    ▶    𝜃    )

Proof

Step	Hyp	Ref	Expression
1		e01.1	⊢ 𝜑
2		e01.2	⊢ (    𝜓    ▶    𝜒    )
3		e01.3	⊢ ( 𝜑 → ( 𝜒 → 𝜃 ) )
4	1	vd01	⊢ (    𝜓    ▶    𝜑    )
5	4 2 3	e11	⊢ (    𝜓    ▶    𝜃    )