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Definition df-1c 4136
Description: Define cardinal one. This is the set of all singletons, or the set of all sets of size one. (Contributed by SF, 12-Jan-2015.)
Assertion
Ref Expression
df-1c 1c = {x y x = {y}}
Distinct variable group:   x,y

Detailed syntax breakdown of Definition df-1c
StepHypRef Expression
1 c1c 4134 . 2 class 1c
2 vx . . . . . 6 setvar x
32cv 1641 . . . . 5 class x
4 vy . . . . . . 7 setvar y
54cv 1641 . . . . . 6 class y
65csn 3737 . . . . 5 class {y}
73, 6wceq 1642 . . . 4 wff x = {y}
87, 4wex 1541 . . 3 wff y x = {y}
98, 2cab 2339 . 2 class {x y x = {y}}
101, 9wceq 1642 1 wff 1c = {x y x = {y}}
Colors of variables: wff setvar class
This definition is referenced by:  el1c  4139  1cex  4142
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