Definition df-gic 19158

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 19156	. 2 class ≃𝑔
2		cgim 19155	. . . 4 class GrpIso
3	2	ccnv 5622	. . 3 class ◡ GrpIso
4		cvv 3438	. . . 4 class V
5		c1o 8388	. . . 4 class 1o
6	4, 5	cdif 3902	. . 3 class (V ∖ 1o)
7	3, 6	cima 5626	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1540	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  19168  gicer  19175