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Mirrors > Home > ILE Home > Th. List > enqbreq | Unicode version |
Description: Equivalence relation for positive fractions in terms of positive integers. (Contributed by NM, 27-Aug-1995.) |
Ref | Expression |
---|---|
enqbreq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-enq 7296 | . 2 | |
2 | 1 | ecopoveq 6604 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 wcel 2141 cop 3584 class class class wbr 3987 (class class class)co 5850 cnpi 7221 cmi 7223 ceq 7228 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-pow 4158 ax-pr 4192 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3566 df-sn 3587 df-pr 3588 df-op 3590 df-uni 3795 df-br 3988 df-opab 4049 df-xp 4615 df-iota 5158 df-fv 5204 df-ov 5853 df-enq 7296 |
This theorem is referenced by: enqbreq2 7306 enqeceq 7308 enqdc 7310 addcmpblnq 7316 mulcmpblnq 7317 mulcanenq 7334 |
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