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Theorem isprm 13073
 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 4208 . . . 4
21rabbidv 2940 . . 3
32breq1d 4214 . 2
4 df-prm 13072 . 2
53, 4elrab2 3086 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   wceq 1652   wcel 1725  crab 2701   class class class wbr 4204  c2o 6710   cen 7098  cn 9992   cdivides 12844  cprime 13071 This theorem is referenced by:  prmnn  13074  1nprm  13076  isprm2  13079 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-prm 13072
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