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Definition df-antisym 5901
 Description: Define the set of all antisymmetric relationships over a base set. (Contributed by SF, 19-Feb-2015.)
Assertion
Ref Expression
df-antisym Antisym = {r, a x a y a ((xry yrx) → x = y)}
Distinct variable group:   r,a,x,y

Detailed syntax breakdown of Definition df-antisym
StepHypRef Expression
1 cantisym 5890 . 2 class Antisym
2 vx . . . . . . . . 9 setvar x
32cv 1641 . . . . . . . 8 class x
4 vy . . . . . . . . 9 setvar y
54cv 1641 . . . . . . . 8 class y
6 vr . . . . . . . . 9 setvar r
76cv 1641 . . . . . . . 8 class r
83, 5, 7wbr 4639 . . . . . . 7 wff xry
95, 3, 7wbr 4639 . . . . . . 7 wff yrx
108, 9wa 358 . . . . . 6 wff (xry yrx)
112, 4weq 1643 . . . . . 6 wff x = y
1210, 11wi 4 . . . . 5 wff ((xry yrx) → x = y)
13 va . . . . . 6 setvar a
1413cv 1641 . . . . 5 class a
1512, 4, 14wral 2614 . . . 4 wff y a ((xry yrx) → x = y)
1615, 2, 14wral 2614 . . 3 wff x a y a ((xry yrx) → x = y)
1716, 6, 13copab 4622 . 2 class {r, a x a y a ((xry yrx) → x = y)}
181, 17wceq 1642 1 wff Antisym = {r, a x a y a ((xry yrx) → x = y)}
 Colors of variables: wff setvar class This definition is referenced by:  antisymex  5912  antird  5928  antid  5929
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