Definition df-gic 19243

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 19241	. 2 class ≃𝑔
2		cgim 19240	. . . 4 class GrpIso
3	2	ccnv 5653	. . 3 class ◡ GrpIso
4		cvv 3459	. . . 4 class V
5		c1o 8473	. . . 4 class 1o
6	4, 5	cdif 3923	. . 3 class (V ∖ 1o)
7	3, 6	cima 5657	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1540	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  19253  gicer  19260