Definition df-gic 19180

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 19178	. 2 class ≃𝑔
2		cgim 19177	. . . 4 class GrpIso
3	2	ccnv 5620	. . 3 class ◡ GrpIso
4		cvv 3437	. . . 4 class V
5		c1o 8387	. . . 4 class 1o
6	4, 5	cdif 3895	. . 3 class (V ∖ 1o)
7	3, 6	cima 5624	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1541	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  19190  gicer  19197