Definition df-gic 19189

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 19187	. 2 class ≃𝑔
2		cgim 19186	. . . 4 class GrpIso
3	2	ccnv 5623	. . 3 class ◡ GrpIso
4		cvv 3440	. . . 4 class V
5		c1o 8390	. . . 4 class 1o
6	4, 5	cdif 3898	. . 3 class (V ∖ 1o)
7	3, 6	cima 5627	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1541	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  19199  gicer  19206