| Colors of
variables: wff
setvar class |
| Syntax hints:
→ wi 4 ∧ wa 394
∈ wcel 2098 ∖
cdif 3937 ‘cfv 6542
ℝcr 11135 ℕcn 12240 ◻NNcsquarenn 42320 Pell1234QRcpell1234qr 42322 Pell14QRcpell14qr 42323 |
| This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905
ax-6 1963 ax-7 2003 ax-8 2100
ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2166 ax-ext 2696 ax-sep 5294 ax-nul 5301 ax-pr 5423 ax-un 7737 ax-cnex 11192 ax-resscn 11193 ax-1cn 11194 ax-icn 11195 ax-addcl 11196 ax-addrcl 11197 ax-mulcl 11198 ax-mulrcl 11199 ax-i2m1 11204 ax-1ne0 11205 ax-rnegex 11207 ax-rrecex 11208 ax-cnre 11209 |
| This theorem depends on definitions:
df-bi 206 df-an 395
df-or 846 df-3or 1085 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2528 df-eu 2557 df-clab 2703 df-cleq 2717 df-clel 2802 df-nfc 2877 df-ne 2931 df-ral 3052 df-rex 3061 df-reu 3365 df-rab 3420 df-v 3465 df-sbc 3770 df-csb 3886 df-dif 3943 df-un 3945 df-in 3947 df-ss 3957 df-pss 3960 df-nul 4319 df-if 4525 df-pw 4600 df-sn 4625 df-pr 4627 df-op 4631 df-uni 4904 df-iun 4993 df-br 5144 df-opab 5206 df-mpt 5227 df-tr 5261 df-id 5570 df-eprel 5576 df-po 5584 df-so 5585 df-fr 5627 df-we 5629 df-xp 5678 df-rel 5679 df-cnv 5680 df-co 5681 df-dm 5682 df-rn 5683 df-res 5684 df-ima 5685 df-pred 6300 df-ord 6367 df-on 6368 df-lim 6369 df-suc 6370 df-iota 6494 df-fun 6544 df-fn 6545 df-f 6546 df-f1 6547 df-fo 6548 df-f1o 6549 df-fv 6550 df-ov 7418 df-om 7868 df-2nd 7990 df-frecs 8283 df-wrecs 8314 df-recs 8388 df-rdg 8427 df-neg 11475 df-nn 12241 df-n0 12501 df-z 12587
df-pell14qr 42327 df-pell1234qr 42328 |
| This theorem is referenced by: pell14qrrp
42344 pell14qrdivcl
42349 pell14qrexpclnn0
42350 pell14qrexpcl
42351 pell14qrdich
42353 elpell1qr2
42356 pell14qrgap
42359 pell14qrgapw
42360 pellfundre
42365 pellfundge
42366 pellfundlb
42368 pellfundglb
42369 pellfundex
42370 pellfund14gap
42371 pellfund14
42382 |
