New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  df-sym GIF version

Definition df-sym 5908
 Description: Define the set of all symmetric relationships over a base set. (Contributed by SF, 19-Feb-2015.)
Assertion
Ref Expression
df-sym Sym = {r, a x a y a (xryyrx)}
Distinct variable group:   r,a,x,y

Detailed syntax breakdown of Definition df-sym
StepHypRef Expression
1 csym 5897 . 2 class Sym
2 vx . . . . . . . 8 setvar x
32cv 1641 . . . . . . 7 class x
4 vy . . . . . . . 8 setvar y
54cv 1641 . . . . . . 7 class y
6 vr . . . . . . . 8 setvar r
76cv 1641 . . . . . . 7 class r
83, 5, 7wbr 4639 . . . . . 6 wff xry
95, 3, 7wbr 4639 . . . . . 6 wff yrx
108, 9wi 4 . . . . 5 wff (xryyrx)
11 va . . . . . 6 setvar a
1211cv 1641 . . . . 5 class a
1310, 4, 12wral 2614 . . . 4 wff y a (xryyrx)
1413, 2, 12wral 2614 . . 3 wff x a y a (xryyrx)
1514, 6, 11copab 4622 . 2 class {r, a x a y a (xryyrx)}
161, 15wceq 1642 1 wff Sym = {r, a x a y a (xryyrx)}
 Colors of variables: wff setvar class This definition is referenced by:  symex  5916  symd  5924  iserd  5942
 Copyright terms: Public domain W3C validator