Theorem climfvd

Description: The limit of a convergent sequence, expressed as the function value of the convergence relation. (Contributed by Glauco Siliprandi, 23-Oct-2021)

	Ref	Expression
Hypothesis	climfvd.1	$$⊢\phi \to F⇝A$$
Assertion	climfvd	$$⊢\phi \to A=⇝\left(F\right)$$

Proof

Step	Hyp	Ref	Expression
1		climfvd.1	$$⊢\phi \to F⇝A$$
2		climfv	$$⊢F⇝A\to A=⇝\left(F\right)$$
3	1 2	syl	$$⊢\phi \to A=⇝\left(F\right)$$