Definition df-gic 19199

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 19197	. 2 class ≃𝑔
2		cgim 19196	. . . 4 class GrpIso
3	2	ccnv 5640	. . 3 class ◡ GrpIso
4		cvv 3450	. . . 4 class V
5		c1o 8430	. . . 4 class 1o
6	4, 5	cdif 3914	. . 3 class (V ∖ 1o)
7	3, 6	cima 5644	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1540	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  19209  gicer  19216