This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem brgric

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

		Ref	Expression
	Assertion	brgric	$⊢ R ≃_{𝑔𝑟} S \leftrightarrow R GraphIso S \neq \emptyset$

Step	Hyp	Ref	Expression
1		df-gric	$⊢ ≃_{𝑔𝑟} = {GraphIso}^{-1} [V ∖ 1_{𝑜}]$
2		grimfn	$⊢ GraphIso Fn (V \times V)$
3	1 2	brwitnlem	$⊢ R ≃_{𝑔𝑟} S \leftrightarrow R GraphIso S \neq \emptyset$