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Definition df-sfin 4446
 Description: Define the finite S relationship. This relationship encapsulates the idea of M being a "smaller" number than N. Definition from [Rosser] p. 530. (Contributed by SF, 12-Jan-2015.)
Assertion
Ref Expression
df-sfin ( Sfin (M, N) ↔ (M Nn N Nn a(1a M a N)))
Distinct variable groups:   M,a   N,a

Detailed syntax breakdown of Definition df-sfin
StepHypRef Expression
1 cM . . 3 class M
2 cN . . 3 class N
31, 2wsfin 4438 . 2 wff Sfin (M, N)
4 cnnc 4373 . . . 4 class Nn
51, 4wcel 1710 . . 3 wff M Nn
62, 4wcel 1710 . . 3 wff N Nn
7 va . . . . . . . 8 setvar a
87cv 1641 . . . . . . 7 class a
98cpw1 4135 . . . . . 6 class 1a
109, 1wcel 1710 . . . . 5 wff 1a M
118cpw 3722 . . . . . 6 class a
1211, 2wcel 1710 . . . . 5 wff a N
1310, 12wa 358 . . . 4 wff (1a M a N)
1413, 7wex 1541 . . 3 wff a(1a M a N)
155, 6, 14w3a 934 . 2 wff (M Nn N Nn a(1a M a N))
163, 15wb 176 1 wff ( Sfin (M, N) ↔ (M Nn N Nn a(1a M a N)))
 Colors of variables: wff setvar class This definition is referenced by:  srelk  4524  sfineq1  4526  sfineq2  4527  sfin01  4528  sfin112  4529  sfindbl  4530  sfintfin  4532  sfinltfin  4535  sfin111  4536  spfinsfincl  4539  vfinspnn  4541  1cvsfin  4542  vfinspsslem1  4550
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