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Mirrors > Home > ILE Home > Th. List > eluz1 | Unicode version |
Description: Membership in the upper
set of integers starting at ![]() |
Ref | Expression |
---|---|
eluz1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uzval 9506 |
. . 3
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2 | 1 | eleq2d 2247 |
. 2
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3 | breq2 4004 |
. . 3
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4 | 3 | elrab 2893 |
. 2
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5 | 2, 4 | bitrdi 196 |
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-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4205 ax-cnex 7880 ax-resscn 7881 |
This theorem depends on definitions: df-bi 117 df-3or 979 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2739 df-sbc 2963 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-opab 4062 df-mpt 4063 df-id 4289 df-xp 4628 df-rel 4629 df-cnv 4630 df-co 4631 df-dm 4632 df-iota 5173 df-fun 5213 df-fv 5219 df-ov 5871 df-neg 8108 df-z 9230 df-uz 9505 |
This theorem is referenced by: eluz2 9510 eluz1i 9511 eluz 9517 uzid 9518 uzss 9524 eluzp1m1 9527 eluzadd 9532 eluzsub 9533 raluz 9554 rexuz 9556 caucvgrelemcau 10960 caucvgre 10961 algcvga 12021 |
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