Definition df-gic 19278

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 19276	. 2 class ≃𝑔
2		cgim 19275	. . . 4 class GrpIso
3	2	ccnv 5684	. . 3 class ◡ GrpIso
4		cvv 3480	. . . 4 class V
5		c1o 8499	. . . 4 class 1o
6	4, 5	cdif 3948	. . 3 class (V ∖ 1o)
7	3, 6	cima 5688	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1540	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  19288  gicer  19295