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Mirrors > Home > ILE Home > Th. List > fzosplitsn | Unicode version |
Description: Extending a half-open range by a singleton on the end. (Contributed by Stefan O'Rear, 23-Aug-2015.) |
Ref | Expression |
---|---|
fzosplitsn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 |
. . . 4
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2 | eluzelz 8921 |
. . . . 5
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3 | uzid 8926 |
. . . . 5
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4 | peano2uz 8964 |
. . . . 5
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5 | 2, 3, 4 | 3syl 17 |
. . . 4
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6 | elfzuzb 9327 |
. . . 4
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7 | 1, 5, 6 | sylanbrc 408 |
. . 3
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8 | fzosplit 9475 |
. . 3
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9 | 7, 8 | syl 14 |
. 2
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10 | fzosn 9503 |
. . . 4
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11 | 2, 10 | syl 14 |
. . 3
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12 | 11 | uneq2d 3138 |
. 2
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13 | 9, 12 | eqtrd 2115 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 577 ax-in2 578 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-13 1445 ax-14 1446 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 ax-sep 3922 ax-pow 3974 ax-pr 3999 ax-un 4223 ax-setind 4315 ax-cnex 7337 ax-resscn 7338 ax-1cn 7339 ax-1re 7340 ax-icn 7341 ax-addcl 7342 ax-addrcl 7343 ax-mulcl 7344 ax-addcom 7346 ax-addass 7348 ax-distr 7350 ax-i2m1 7351 ax-0lt1 7352 ax-0id 7354 ax-rnegex 7355 ax-cnre 7357 ax-pre-ltirr 7358 ax-pre-ltwlin 7359 ax-pre-lttrn 7360 ax-pre-apti 7361 ax-pre-ltadd 7362 |
This theorem depends on definitions: df-bi 115 df-3or 921 df-3an 922 df-tru 1288 df-fal 1291 df-nf 1391 df-sb 1688 df-eu 1946 df-mo 1947 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-ne 2250 df-nel 2345 df-ral 2358 df-rex 2359 df-reu 2360 df-rab 2362 df-v 2614 df-sbc 2827 df-csb 2920 df-dif 2986 df-un 2988 df-in 2990 df-ss 2997 df-pw 3408 df-sn 3428 df-pr 3429 df-op 3431 df-uni 3628 df-int 3663 df-iun 3706 df-br 3812 df-opab 3866 df-mpt 3867 df-id 4083 df-xp 4405 df-rel 4406 df-cnv 4407 df-co 4408 df-dm 4409 df-rn 4410 df-res 4411 df-ima 4412 df-iota 4932 df-fun 4969 df-fn 4970 df-f 4971 df-fv 4975 df-riota 5545 df-ov 5592 df-oprab 5593 df-mpt2 5594 df-1st 5844 df-2nd 5845 df-pnf 7425 df-mnf 7426 df-xr 7427 df-ltxr 7428 df-le 7429 df-sub 7556 df-neg 7557 df-inn 8315 df-n0 8564 df-z 8645 df-uz 8913 df-fz 9318 df-fzo 9442 |
This theorem is referenced by: fzosplitprm1 9532 fzosplitsni 9533 fzisfzounsn 9534 |
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