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Mirrors > Home > ILE Home > Th. List > 1nq | Unicode version |
Description: The positive fraction 'one'. (Contributed by NM, 29-Oct-1995.) |
Ref | Expression |
---|---|
1nq |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1pi 7345 |
. . . 4
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2 | opelxpi 4676 |
. . . 4
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3 | 1, 1, 2 | mp2an 426 |
. . 3
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4 | enqex 7390 |
. . . 4
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5 | 4 | ecelqsi 6616 |
. . 3
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6 | 3, 5 | ax-mp 5 |
. 2
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7 | df-1nqqs 7381 |
. 2
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8 | df-nqqs 7378 |
. 2
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9 | 6, 7, 8 | 3eltr4i 2271 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-nul 4144 ax-pow 4192 ax-pr 4227 ax-un 4451 ax-iinf 4605 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ne 2361 df-ral 2473 df-rex 2474 df-v 2754 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-nul 3438 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-int 3860 df-br 4019 df-opab 4080 df-suc 4389 df-iom 4608 df-xp 4650 df-cnv 4652 df-dm 4654 df-rn 4655 df-res 4656 df-ima 4657 df-1o 6442 df-ec 6562 df-qs 6566 df-ni 7334 df-enq 7377 df-nqqs 7378 df-1nqqs 7381 |
This theorem is referenced by: recmulnqg 7421 rec1nq 7425 ltaddnq 7437 halfnqq 7440 addnqprllem 7557 addnqprulem 7558 1pr 7584 addnqpr1 7592 appdivnq 7593 1idprl 7620 1idpru 7621 recexprlemm 7654 recexprlem1ssl 7663 recexprlem1ssu 7664 cauappcvgprlemm 7675 caucvgprlemm 7698 caucvgprprlemmu 7725 suplocexprlemmu 7748 |
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