Definition df-gic 19167

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 19165	. 2 class ≃𝑔
2		cgim 19164	. . . 4 class GrpIso
3	2	ccnv 5610	. . 3 class ◡ GrpIso
4		cvv 3436	. . . 4 class V
5		c1o 8373	. . . 4 class 1o
6	4, 5	cdif 3894	. . 3 class (V ∖ 1o)
7	3, 6	cima 5614	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1541	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  19177  gicer  19184