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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 7065 |
. . . 4
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2 | opelxpi 4529 |
. . . 4
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3 | 1, 1, 2 | mp2an 420 |
. . 3
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4 | enqex 7110 |
. . . 4
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5 | 4 | ecelqsi 6435 |
. . 3
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6 | 3, 5 | ax-mp 7 |
. 2
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7 | df-1nqqs 7101 |
. 2
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8 | df-nqqs 7098 |
. 2
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9 | 6, 7, 8 | 3eltr4i 2194 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 586 ax-in2 587 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-13 1472 ax-14 1473 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 ax-sep 4004 ax-nul 4012 ax-pow 4056 ax-pr 4089 ax-un 4313 ax-iinf 4460 |
This theorem depends on definitions: df-bi 116 df-3an 945 df-tru 1315 df-nf 1418 df-sb 1717 df-eu 1976 df-mo 1977 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-ne 2281 df-ral 2393 df-rex 2394 df-v 2657 df-dif 3037 df-un 3039 df-in 3041 df-ss 3048 df-nul 3328 df-pw 3476 df-sn 3497 df-pr 3498 df-op 3500 df-uni 3701 df-int 3736 df-br 3894 df-opab 3948 df-suc 4251 df-iom 4463 df-xp 4503 df-cnv 4505 df-dm 4507 df-rn 4508 df-res 4509 df-ima 4510 df-1o 6265 df-ec 6383 df-qs 6387 df-ni 7054 df-enq 7097 df-nqqs 7098 df-1nqqs 7101 |
This theorem is referenced by: recmulnqg 7141 rec1nq 7145 ltaddnq 7157 halfnqq 7160 addnqprllem 7277 addnqprulem 7278 1pr 7304 addnqpr1 7312 appdivnq 7313 1idprl 7340 1idpru 7341 recexprlemm 7374 recexprlem1ssl 7383 recexprlem1ssu 7384 cauappcvgprlemm 7395 caucvgprlemm 7418 caucvgprprlemmu 7445 |
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