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Definition df-lefin 4440
 Description: Define the less than or equal to relationship for finite cardinals. Definition from Ex. X.1.4 of [Rosser] p. 279. (Contributed by SF, 12-Jan-2015.)
Assertion
Ref Expression
df-lefin fin = {x yz(x = ⟪y, z w Nn z = (y +c w))}
Distinct variable group:   x,y,z,w

Detailed syntax breakdown of Definition df-lefin
StepHypRef Expression
1 clefin 4432 . 2 class fin
2 vx . . . . . . . 8 setvar x
32cv 1641 . . . . . . 7 class x
4 vy . . . . . . . . 9 setvar y
54cv 1641 . . . . . . . 8 class y
6 vz . . . . . . . . 9 setvar z
76cv 1641 . . . . . . . 8 class z
85, 7copk 4057 . . . . . . 7 class y, z
93, 8wceq 1642 . . . . . 6 wff x = ⟪y, z
10 vw . . . . . . . . . 10 setvar w
1110cv 1641 . . . . . . . . 9 class w
125, 11cplc 4375 . . . . . . . 8 class (y +c w)
137, 12wceq 1642 . . . . . . 7 wff z = (y +c w)
14 cnnc 4373 . . . . . . 7 class Nn
1513, 10, 14wrex 2615 . . . . . 6 wff w Nn z = (y +c w)
169, 15wa 358 . . . . 5 wff (x = ⟪y, z w Nn z = (y +c w))
1716, 6wex 1541 . . . 4 wff z(x = ⟪y, z w Nn z = (y +c w))
1817, 4wex 1541 . . 3 wff yz(x = ⟪y, z w Nn z = (y +c w))
1918, 2cab 2339 . 2 class {x yz(x = ⟪y, z w Nn z = (y +c w))}
201, 19wceq 1642 1 wff fin = {x yz(x = ⟪y, z w Nn z = (y +c w))}
 Colors of variables: wff setvar class This definition is referenced by:  opklefing  4448
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