Definition df-gic 19467

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 19465	. 2 class ≃𝑔
2		cgim 19464	. . . 4 class GrpIso
3	2	ccnv 5650	. . 3 class ◡ GrpIso
4		cvv 3451	. . . 4 class V
5		c1o 8462	. . . 4 class 1o
6	4, 5	cdif 3896	. . 3 class (V ∖ 1o)
7	3, 6	cima 5654	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1570	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is used by:  brgic  19477  gicer  19484