Definition df-gic 19213

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 19211	. 2 class ≃𝑔
2		cgim 19210	. . . 4 class GrpIso
3	2	ccnv 5677	. . 3 class ◡ GrpIso
4		cvv 3471	. . . 4 class V
5		c1o 8479	. . . 4 class 1o
6	4, 5	cdif 3944	. . 3 class (V ∖ 1o)
7	3, 6	cima 5681	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1534	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  19223  gicer  19230