Definition df-gic 17702

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 17700	. 2 class ≃𝑔
2		cgim 17699	. . . 4 class GrpIso
3	2	ccnv 5113	. . 3 class ◡ GrpIso
4		cvv 3200	. . . 4 class V
5		c1o 7553	. . . 4 class 1𝑜
6	4, 5	cdif 3571	. . 3 class (V ∖ 1𝑜)
7	3, 6	cima 5117	. 2 class (◡ GrpIso “ (V ∖ 1𝑜))
8	1, 7	wceq 1483	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1𝑜))

This definition is referenced by:  brgic  17711  gicer  17718  gicerOLD  17719