Definition df-gic 19133

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 19131	. 2 class ≃𝑔
2		cgim 19130	. . . 4 class GrpIso
3	2	ccnv 5675	. . 3 class ◡ GrpIso
4		cvv 3474	. . . 4 class V
5		c1o 8458	. . . 4 class 1o
6	4, 5	cdif 3945	. . 3 class (V ∖ 1o)
7	3, 6	cima 5679	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1541	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  19142  gicer  19149