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Definition df-spfin 4447
 Description: Define the finite Sp set. Definition from [Rosser] p. 533. (Contributed by SF, 12-Jan-2015.)
Assertion
Ref Expression
df-spfin Spfin = {a ( Ncfin V a x a z( Sfin (z, x) → z a))}
Distinct variable group:   x,a,z

Detailed syntax breakdown of Definition df-spfin
StepHypRef Expression
1 cspfin 4439 . 2 class Spfin
2 cvv 2859 . . . . . . 7 class V
32cncfin 4434 . . . . . 6 class Ncfin V
4 va . . . . . . 7 setvar a
54cv 1641 . . . . . 6 class a
63, 5wcel 1710 . . . . 5 wff Ncfin V a
7 vz . . . . . . . . . 10 setvar z
87cv 1641 . . . . . . . . 9 class z
9 vx . . . . . . . . . 10 setvar x
109cv 1641 . . . . . . . . 9 class x
118, 10wsfin 4438 . . . . . . . 8 wff Sfin (z, x)
127, 4wel 1711 . . . . . . . 8 wff z a
1311, 12wi 4 . . . . . . 7 wff ( Sfin (z, x) → z a)
1413, 7wal 1540 . . . . . 6 wff z( Sfin (z, x) → z a)
1514, 9, 5wral 2614 . . . . 5 wff x a z( Sfin (z, x) → z a)
166, 15wa 358 . . . 4 wff ( Ncfin V a x a z( Sfin (z, x) → z a))
1716, 4cab 2339 . . 3 class {a ( Ncfin V a x a z( Sfin (z, x) → z a))}
1817cint 3926 . 2 class {a ( Ncfin V a x a z( Sfin (z, x) → z a))}
191, 18wceq 1642 1 wff Spfin = {a ( Ncfin V a x a z( Sfin (z, x) → z a))}
 Colors of variables: wff setvar class This definition is referenced by:  spfinex  4537  ncvspfin  4538  spfinsfincl  4539  spfininduct  4540
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