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Metamath Proof Explorer

Theorem brgrici

Description: Prove that two graphs are isomorphic by an explicit isomorphism. (Contributed by AV, 28-Apr-2025)

		Ref	Expression
	Assertion	brgrici	$⊢ F \in (R GraphIso S) \to R ≃_{𝑔𝑟} S$

Step	Hyp	Ref	Expression
1		ne0i	$⊢ F \in (R GraphIso S) \to R GraphIso S \neq \emptyset$
2		brgric	$⊢ R ≃_{𝑔𝑟} S \leftrightarrow R GraphIso S \neq \emptyset$
3	1 2	sylibr	$⊢ F \in (R GraphIso S) \to R ≃_{𝑔𝑟} S$