Definition df-gic 19168

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 19166	. 2 class ≃𝑔
2		cgim 19165	. . . 4 class GrpIso
3	2	ccnv 5630	. . 3 class ◡ GrpIso
4		cvv 3444	. . . 4 class V
5		c1o 8404	. . . 4 class 1o
6	4, 5	cdif 3908	. . 3 class (V ∖ 1o)
7	3, 6	cima 5634	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1540	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  19178  gicer  19185