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Theorem pell1234qrre 26896
 Description: General Pell solutions are (coded as) real numbers. (Contributed by Stefan O'Rear, 17-Sep-2014.)
Assertion
Ref Expression
pell1234qrre NN Pell1234QR

Proof of Theorem pell1234qrre
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 elpell1234qr 26895 . 2 NN Pell1234QR
21simprbda 607 1 NN Pell1234QR
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725  wrex 2698   cdif 3309  cfv 5446  (class class class)co 6073  cr 8981  c1 8983   caddc 8985   cmul 8987   cmin 9283  cn 9992  c2 10041  cz 10274  cexp 11374  csqr 12030  ◻NNcsquarenn 26880  Pell1234QRcpell1234qr 26882 This theorem is referenced by:  pell1234qrreccl  26898  pell14qrre  26901  elpell14qr2  26906  pell14qrmulcl  26907  pell14qrreccl  26908 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395  ax-cnex 9038  ax-resscn 9039 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-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  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-uni 4008  df-br 4205  df-opab 4259  df-mpt 4260  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-iota 5410  df-fun 5448  df-fv 5454  df-ov 6076  df-pell1234qr 26888
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