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Metamath Proof Explorer

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	$⊢ φ \to F ⇝ A$
	Assertion	climfvd	$⊢ φ \to A = ⇝ (F)$

Proof

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