Theorem e11

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 14-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e11.1	⊢ (    𝜑    ▶    𝜓    )
	e11.2	⊢ (    𝜑    ▶    𝜒    )
	e11.3	⊢ ( 𝜓 → ( 𝜒 → 𝜃 ) )
Assertion	e11	⊢ (    𝜑    ▶    𝜃    )

Proof

Step	Hyp	Ref	Expression
1		e11.1	⊢ (    𝜑    ▶    𝜓    )
2		e11.2	⊢ (    𝜑    ▶    𝜒    )
3		e11.3	⊢ ( 𝜓 → ( 𝜒 → 𝜃 ) )
4	3	a1i	⊢ ( 𝜓 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
5	1 1 2 4	e111	⊢ (    𝜑    ▶    𝜃    )