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Theorem isprm 10716
 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 3809 . . . 4
21rabbidv 2599 . . 3
32breq1d 3815 . 2
4 df-prm 10715 . 2
53, 4elrab2 2760 1
 Colors of variables: wff set class Syntax hints:   wa 102   wb 103   wceq 1285   wcel 1434  crab 2357   class class class wbr 3805  c2o 6080   cen 6307  cn 8176   cdvds 10421  cprime 10714 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-rab 2362  df-v 2612  df-un 2986  df-sn 3422  df-pr 3423  df-op 3425  df-br 3806  df-prm 10715 This theorem is referenced by:  prmnn  10717  1nprm  10721  isprm2  10724
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