Definition df-gic 18184

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 18182	. 2 class ≃𝑔
2		cgim 18181	. . . 4 class GrpIso
3	2	ccnv 5403	. . 3 class ◡ GrpIso
4		cvv 3410	. . . 4 class V
5		c1o 7897	. . . 4 class 1o
6	4, 5	cdif 3821	. . 3 class (V ∖ 1o)
7	3, 6	cima 5407	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1508	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  18193  gicer  18200