Definition df-gic 19374

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 19372	. 2 class ≃𝑔
2		cgim 19371	. . . 4 class GrpIso
3	2	ccnv 5662	. . 3 class ◡ GrpIso
4		cvv 3457	. . . 4 class V
5		c1o 8452	. . . 4 class 1o
6	4, 5	cdif 3903	. . 3 class (V ∖ 1o)
7	3, 6	cima 5666	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1570	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is used by:  brgic  19384  gicer  19391