Definition df-gic 19235

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 19233	. 2 class ≃𝑔
2		cgim 19232	. . . 4 class GrpIso
3	2	ccnv 5630	. . 3 class ◡ GrpIso
4		cvv 3429	. . . 4 class V
5		c1o 8398	. . . 4 class 1o
6	4, 5	cdif 3886	. . 3 class (V ∖ 1o)
7	3, 6	cima 5634	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1542	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  19245  gicer  19252