Definition df-gic 19226

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 19224	. 2 class ≃𝑔
2		cgim 19223	. . . 4 class GrpIso
3	2	ccnv 5623	. . 3 class ◡ GrpIso
4		cvv 3430	. . . 4 class V
5		c1o 8391	. . . 4 class 1o
6	4, 5	cdif 3887	. . 3 class (V ∖ 1o)
7	3, 6	cima 5627	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1542	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  19236  gicer  19243