Definition df-gic 19326

Description: Two groups are said to be isomorphic iff they are connected by at least one isomorphism. Isomorphic groups share all global group properties, but to relate local properties requires knowledge of a specific isomorphism. (Contributed by Stefan O'Rear, 25-Jan-2015.)

Assertion

Ref	Expression
df-gic	⊢ ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

Detailed syntax breakdown of Definition df-gic

Step	Hyp	Ref	Expression
1		cgic 19324	. 2 class ≃𝑔
2		cgim 19323	. . . 4 class GrpIso
3	2	ccnv 5658	. . 3 class ◡ GrpIso
4		cvv 3463	. . . 4 class V
5		c1o 8442	. . . 4 class 1o
6	4, 5	cdif 3910	. . 3 class (V ∖ 1o)
7	3, 6	cima 5662	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1567	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  19336  gicer  19343