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Mirrors > Home > ILE Home > Th. List > elfzel2 | Unicode version |
Description: Membership in a finite set of sequential integer implies the upper bound is an integer. (Contributed by NM, 6-Sep-2005.) (Revised by Mario Carneiro, 28-Apr-2015.) |
Ref | Expression |
---|---|
elfzel2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elfzuz3 10051 |
. 2
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2 | eluzelz 9566 |
. 2
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3 | 1, 2 | syl 14 |
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-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 ax-setind 4554 ax-cnex 7931 ax-resscn 7932 |
This theorem depends on definitions: df-bi 117 df-3or 981 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ne 2361 df-ral 2473 df-rex 2474 df-rab 2477 df-v 2754 df-sbc 2978 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-mpt 4081 df-id 4311 df-xp 4650 df-rel 4651 df-cnv 4652 df-co 4653 df-dm 4654 df-rn 4655 df-res 4656 df-ima 4657 df-iota 5196 df-fun 5237 df-fn 5238 df-f 5239 df-fv 5243 df-ov 5898 df-oprab 5899 df-mpo 5900 df-neg 8160 df-z 9283 df-uz 9558 df-fz 10038 |
This theorem is referenced by: elfz1eq 10064 fzdisj 10081 fzssp1 10096 fzp1disj 10109 fzrev2i 10115 fzrev3 10116 fznuz 10131 fznn0sub2 10157 elfzmlbm 10160 difelfznle 10164 nn0disj 10167 fzofzp1b 10257 iseqf1olemqcl 10516 iseqf1olemab 10519 iseqf1olemqf1o 10523 iseqf1olemqk 10524 iseqf1olemjpcl 10525 iseqf1olemqpcl 10526 iseqf1olemfvp 10527 seq3f1olemqsumkj 10528 seq3f1olemqsumk 10529 seq3f1olemqsum 10530 seq3f1olemstep 10531 bcm1k 10771 bcp1nk 10773 |
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