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Theorem isprm 14703
 Description: The predicate "is a prime number". A prime number is a positive integer with exactly two positive divisors. (Contributed by Paul Chapman, 22-Jun-2011.)
Assertion
Ref Expression
isprm
Distinct variable group:   ,

Proof of Theorem isprm
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 breq2 4399 . . . 4
21rabbidv 3022 . . 3
32breq1d 4405 . 2
4 df-prm 14702 . 2
53, 4elrab2 3186 1
 Colors of variables: wff setvar class Syntax hints:   wb 189   wa 376   wceq 1452   wcel 1904  crab 2760   class class class wbr 4395  c2o 7194   cen 7584  cn 10631   cdvds 14382  cprime 14701 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ral 2761  df-rab 2765  df-v 3033  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-br 4396  df-prm 14702 This theorem is referenced by:  prmnn  14704  1nprm  14708  isprm2  14711
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