Definition df-gic 18791

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 18789	. 2 class ≃𝑔
2		cgim 18788	. . . 4 class GrpIso
3	2	ccnv 5579	. . 3 class ◡ GrpIso
4		cvv 3422	. . . 4 class V
5		c1o 8260	. . . 4 class 1o
6	4, 5	cdif 3880	. . 3 class (V ∖ 1o)
7	3, 6	cima 5583	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1539	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  18800  gicer  18807