Theorem brgrilci

Description: Prove that two graphs are locally isomorphic by an explicit local isomorphism. (Contributed by AV, 9-Jun-2025)

	Ref	Expression
Assertion	brgrilci	⊢ ( 𝐹 ∈ ( 𝑅 GraphLocIso 𝑆 ) → 𝑅 ≃𝑙𝑔𝑟 𝑆 )

Proof

Step	Hyp	Ref	Expression
1		ne0i	⊢ ( 𝐹 ∈ ( 𝑅 GraphLocIso 𝑆 ) → ( 𝑅 GraphLocIso 𝑆 ) ≠ ∅ )
2		brgrlic	⊢ ( 𝑅 ≃𝑙𝑔𝑟 𝑆 ↔ ( 𝑅 GraphLocIso 𝑆 ) ≠ ∅ )
3	1 2	sylibr	⊢ ( 𝐹 ∈ ( 𝑅 GraphLocIso 𝑆 ) → 𝑅 ≃𝑙𝑔𝑟 𝑆 )