Theorem e10

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

	Ref	Expression
Hypotheses	e10.1	⊢ (    𝜑    ▶    𝜓    )
	e10.2	⊢ 𝜒
	e10.3	⊢ ( 𝜓 → ( 𝜒 → 𝜃 ) )
Assertion	e10	⊢ (    𝜑    ▶    𝜃    )

Proof

Step	Hyp	Ref	Expression
1		e10.1	⊢ (    𝜑    ▶    𝜓    )
2		e10.2	⊢ 𝜒
3		e10.3	⊢ ( 𝜓 → ( 𝜒 → 𝜃 ) )
4	2	vd01	⊢ (    𝜑    ▶    𝜒    )
5	1 4 3	e11	⊢ (    𝜑    ▶    𝜃    )