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Mirrors > Home > ILE Home > Th. List > seqex | Unicode version |
Description: Existence of the sequence builder operation. (Contributed by Mario Carneiro, 4-Sep-2013.) |
Ref | Expression |
---|---|
seqex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-seqfrec 10479 |
. 2
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2 | frecex 6420 |
. . 3
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3 | 2 | rnex 4912 |
. 2
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4 | 1, 3 | eqeltri 2262 |
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 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-13 2162 ax-14 2163 ax-ext 2171 ax-coll 4133 ax-sep 4136 ax-pow 4192 ax-pr 4227 ax-un 4451 ax-setind 4554 ax-iinf 4605 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 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-ral 2473 df-rex 2474 df-reu 2475 df-rab 2477 df-v 2754 df-sbc 2978 df-csb 3073 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-int 3860 df-iun 3903 df-br 4019 df-opab 4080 df-mpt 4081 df-tr 4117 df-id 4311 df-iord 4384 df-on 4386 df-iom 4608 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-f1 5240 df-fo 5241 df-f1o 5242 df-fv 5243 df-recs 6331 df-frec 6417 df-seqfrec 10479 |
This theorem is referenced by: seq3shft 10882 clim2ser 11380 clim2ser2 11381 isermulc2 11383 iser3shft 11389 fsum3cvg 11421 sumrbdc 11422 isumclim3 11466 sumnul 11467 isumadd 11474 trireciplem 11543 geolim 11554 geolim2 11555 geo2lim 11559 geoisum1c 11563 mertensabs 11580 clim2prod 11582 clim2divap 11583 ntrivcvgap 11591 fproddccvg 11615 prodrbdclem2 11616 fprodntrivap 11627 efcj 11716 eftlub 11733 eflegeo 11744 nninfdc 12507 gsumval2 12875 mulgfvalg 13078 trilpolemisumle 15265 trilpolemeq1 15267 |
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