Definition df-gic 19201

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 19199	. 2 class ≃𝑔
2		cgim 19198	. . . 4 class GrpIso
3	2	ccnv 5631	. . 3 class ◡ GrpIso
4		cvv 3442	. . . 4 class V
5		c1o 8400	. . . 4 class 1o
6	4, 5	cdif 3900	. . 3 class (V ∖ 1o)
7	3, 6	cima 5635	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1542	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  19211  gicer  19218