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Theorem pell1qrval 26910
 Description: Value of the set of first-quadrant Pell solutions. (Contributed by Stefan O'Rear, 17-Sep-2014.)
Assertion
Ref Expression
pell1qrval NN Pell1QR
Distinct variable group:   ,,,

Proof of Theorem pell1qrval
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 fveq2 5729 . . . . . . . 8
21oveq1d 6097 . . . . . . 7
32oveq2d 6098 . . . . . 6
43eqeq2d 2448 . . . . 5
5 oveq1 6089 . . . . . . 7
65oveq2d 6098 . . . . . 6
76eqeq1d 2445 . . . . 5
84, 7anbi12d 693 . . . 4
982rexbidv 2749 . . 3
109rabbidv 2949 . 2
11 df-pell1qr 26906 . 2 Pell1QR NN
12 reex 9082 . . 3
1312rabex 4355 . 2
1410, 11, 13fvmpt 5807 1 NN Pell1QR
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726  wrex 2707  crab 2710   cdif 3318  cfv 5455  (class class class)co 6082  cr 8990  c1 8992   caddc 8994   cmul 8996   cmin 9292  cn 10001  c2 10050  cn0 10222  cexp 11383  csqr 12039  ◻NNcsquarenn 26900  Pell1QRcpell1qr 26901 This theorem is referenced by:  elpell1qr  26911 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418  ax-sep 4331  ax-nul 4339  ax-pr 4404  ax-cnex 9047  ax-resscn 9048 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2286  df-mo 2287  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-ral 2711  df-rex 2712  df-rab 2715  df-v 2959  df-sbc 3163  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824  df-uni 4017  df-br 4214  df-opab 4268  df-mpt 4269  df-id 4499  df-xp 4885  df-rel 4886  df-cnv 4887  df-co 4888  df-dm 4889  df-iota 5419  df-fun 5457  df-fv 5463  df-ov 6085  df-pell1qr 26906
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