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Mirrors > Home > ILE Home > Th. List > uztrn2 | Unicode version |
Description: Transitive law for sets of upper integers. (Contributed by Mario Carneiro, 26-Dec-2013.) |
Ref | Expression |
---|---|
uztrn2.1 |
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Ref | Expression |
---|---|
uztrn2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uztrn2.1 |
. . . 4
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2 | 1 | eleq2i 2207 |
. . 3
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3 | uztrn 9366 |
. . . 4
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4 | 3 | ancoms 266 |
. . 3
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5 | 2, 4 | sylanb 282 |
. 2
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6 | 5, 1 | eleqtrrdi 2234 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 ax-un 4363 ax-setind 4460 ax-cnex 7735 ax-resscn 7736 ax-pre-ltwlin 7757 |
This theorem depends on definitions: df-bi 116 df-3or 964 df-3an 965 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ne 2310 df-nel 2405 df-ral 2422 df-rex 2423 df-rab 2426 df-v 2691 df-sbc 2914 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-mpt 3999 df-id 4223 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-rn 4558 df-res 4559 df-ima 4560 df-iota 5096 df-fun 5133 df-fn 5134 df-f 5135 df-fv 5139 df-ov 5785 df-pnf 7826 df-mnf 7827 df-xr 7828 df-ltxr 7829 df-le 7830 df-neg 7960 df-z 9079 df-uz 9351 |
This theorem is referenced by: eluznn0 9420 eluznn 9421 elfzuz2 9840 rexuz3 10794 r19.29uz 10796 r19.2uz 10797 clim2 11084 clim2c 11085 clim0c 11087 2clim 11102 climabs0 11108 climcn1 11109 climcn2 11110 climsqz 11136 climsqz2 11137 clim2ser 11138 clim2ser2 11139 climub 11145 serf0 11153 mertenslemi1 11336 clim2divap 11341 lmbrf 12423 lmss 12454 lmres 12456 txlm 12487 |
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