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Mirrors > Home > ILE Home > Th. List > enqex | Unicode version |
Description: The equivalence relation for positive fractions exists. (Contributed by NM, 3-Sep-1995.) |
Ref | Expression |
---|---|
enqex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | niex 6410 | . . . 4 | |
2 | 1, 1 | xpex 4453 | . . 3 |
3 | 2, 2 | xpex 4453 | . 2 |
4 | df-enq 6445 | . . 3 | |
5 | opabssxp 4414 | . . 3 | |
6 | 4, 5 | eqsstri 2975 | . 2 |
7 | 3, 6 | ssexi 3895 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wceq 1243 wex 1381 wcel 1393 cvv 2557 cop 3378 copab 3817 cxp 4343 (class class class)co 5512 cnpi 6370 cmi 6372 ceq 6377 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-13 1404 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 ax-un 4170 ax-iinf 4311 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-dif 2920 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-int 3616 df-opab 3819 df-iom 4314 df-xp 4351 df-ni 6402 df-enq 6445 |
This theorem is referenced by: 1nq 6464 addpipqqs 6468 mulpipqqs 6471 ordpipqqs 6472 addclnq 6473 mulclnq 6474 dmaddpq 6477 dmmulpq 6478 recexnq 6488 ltexnqq 6506 prarloclemarch 6516 prarloclemarch2 6517 nnnq 6520 nqpnq0nq 6551 prarloclemlt 6591 prarloclemlo 6592 prarloclemcalc 6600 nqprm 6640 |
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