Definition df-gic 18876

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 18874	. 2 class ≃𝑔
2		cgim 18873	. . . 4 class GrpIso
3	2	ccnv 5588	. . 3 class ◡ GrpIso
4		cvv 3432	. . . 4 class V
5		c1o 8290	. . . 4 class 1o
6	4, 5	cdif 3884	. . 3 class (V ∖ 1o)
7	3, 6	cima 5592	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1539	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  18885  gicer  18892