Definition df-gic 19483

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 19481	. 2 class ≃𝑔
2		cgim 19480	. . . 4 class GrpIso
3	2	ccnv 5650	. . 3 class ◡ GrpIso
4		cvv 3450	. . . 4 class V
5		c1o 8476	. . . 4 class 1o
6	4, 5	cdif 4044	. . 3 class (V ∖ 1o)
7	3, 6	cima 5654	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1569	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is used by:  brgic  19493  gicer  19500