Definition df-gic 19226

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 19224	. 2 class ≃𝑔
2		cgim 19223	. . . 4 class GrpIso
3	2	ccnv 5617	. . 3 class ◡ GrpIso
4		cvv 3431	. . . 4 class V
5		c1o 8388	. . . 4 class 1o
6	4, 5	cdif 3880	. . 3 class (V ∖ 1o)
7	3, 6	cima 5621	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1547	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  19236  gicer  19243