Definition df-gic 19192

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 19190	. 2 class ≃𝑔
2		cgim 19189	. . . 4 class GrpIso
3	2	ccnv 5637	. . 3 class ◡ GrpIso
4		cvv 3447	. . . 4 class V
5		c1o 8427	. . . 4 class 1o
6	4, 5	cdif 3911	. . 3 class (V ∖ 1o)
7	3, 6	cima 5641	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1540	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  19202  gicer  19209