Definition df-gic 19325

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 19323	. 2 class ≃𝑔
2		cgim 19322	. . . 4 class GrpIso
3	2	ccnv 5660	. . 3 class ◡ GrpIso
4		cvv 3455	. . . 4 class V
5		c1o 8442	. . . 4 class 1o
6	4, 5	cdif 3902	. . 3 class (V ∖ 1o)
7	3, 6	cima 5664	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1570	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  19335  gicer  19342