Theorem brgric

Description: The relation "is isomorphic to" for graphs. (Contributed by AV, 28-Apr-2025)

	Ref	Expression
Assertion	brgric	⊢ ( 𝑅 ≃𝑔𝑟 𝑆 ↔ ( 𝑅 GraphIso 𝑆 ) ≠ ∅ )

Proof

Step	Hyp	Ref	Expression
1		df-gric	⊢ ≃𝑔𝑟 = ( ◡ GraphIso “ ( V ∖ 1o ) )
2		grimfn	⊢ GraphIso Fn ( V × V )
3	1 2	brwitnlem	⊢ ( 𝑅 ≃𝑔𝑟 𝑆 ↔ ( 𝑅 GraphIso 𝑆 ) ≠ ∅ )