Colors of
variables: wff
setvar class |
Syntax hints:
โ wi 4 โง wa 397
= wceq 1542 โ
wcel 2107 โwrex 3070
โ cdif 3911 โcfv 6500 (class class class)co 7361
โcr 11058 1c1 11060
+ caddc 11062 ยท
cmul 11064 โ cmin 11393
โcn 12161 2c2 12216
โคcz 12507 โcexp 13976 โcsqrt 15127 โปNNcsquarenn 41206 Pell1234QRcpell1234qr 41208 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914
ax-6 1972 ax-7 2012 ax-8 2109
ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 ax-sep 5260 ax-nul 5267 ax-pr 5388 ax-cnex 11115 ax-resscn 11116 |
This theorem depends on definitions:
df-bi 206 df-an 398
df-or 847 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ral 3062 df-rex 3071 df-rab 3407 df-v 3449 df-dif 3917 df-un 3919 df-in 3921 df-ss 3931 df-nul 4287 df-if 4491 df-sn 4591 df-pr 4593 df-op 4597 df-uni 4870 df-br 5110 df-opab 5172 df-mpt 5193 df-id 5535 df-xp 5643 df-rel 5644 df-cnv 5645 df-co 5646 df-dm 5647 df-iota 6452 df-fun 6502 df-fv 6508 df-ov 7364 df-pell1234qr 41214 |
This theorem is referenced by: pell1234qrreccl
41224 pell14qrre
41227 elpell14qr2
41232 pell14qrmulcl
41233 pell14qrreccl
41234 |