Definition df-gric 47867

Description: Two graphs are said to be isomorphic iff they are connected by at least one isomorphism, see definition in [Diestel] p. 3 and definition in [Bollobas] p. 3. Isomorphic graphs share all global graph properties like order and size. (Contributed by AV, 11-Nov-2022.) (Revised by AV, 19-Apr-2025.)

Assertion

Ref	Expression
df-gric	⊢ ≃𝑔𝑟 = (◡ GraphIso “ (V ∖ 1o))

Detailed syntax breakdown of Definition df-gric

Step	Hyp	Ref	Expression
1		cgric 47862	. 2 class ≃𝑔𝑟
2		cgrim 47861	. . . 4 class GraphIso
3	2	ccnv 5684	. . 3 class ◡ GraphIso
4		cvv 3480	. . . 4 class V
5		c1o 8499	. . . 4 class 1o
6	4, 5	cdif 3948	. . 3 class (V ∖ 1o)
7	3, 6	cima 5688	. 2 class (◡ GraphIso “ (V ∖ 1o))
8	1, 7	wceq 1540	1 wff ≃𝑔𝑟 = (◡ GraphIso “ (V ∖ 1o))

This definition is referenced by:  brgric  47881  gricrel  47888