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Mirrors > Home > ILE Home > Th. List > seqeq3d | Unicode version |
Description: Equality deduction for the sequence builder operation. (Contributed by Mario Carneiro, 7-Sep-2013.) |
Ref | Expression |
---|---|
seqeqd.1 |
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Ref | Expression |
---|---|
seqeq3d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | seqeqd.1 |
. 2
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2 | seqeq3 10480 |
. 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-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-ext 2171 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-mpt 4081 df-cnv 4652 df-dm 4654 df-rn 4655 df-res 4656 df-iota 5196 df-fv 5243 df-ov 5898 df-oprab 5899 df-mpo 5900 df-recs 6329 df-frec 6415 df-seqfrec 10476 |
This theorem is referenced by: seqeq123d 10484 seq3f1olemstep 10531 seq3f1olemp 10532 exp3val 10552 sumeq1 11394 sumeq2 11398 summodc 11422 zsumdc 11423 fsum3 11426 isumz 11428 prodeq1f 11591 prodeq2w 11595 prodeq2 11596 prodmodc 11617 zproddc 11618 fprodseq 11622 prod1dc 11625 mulgval 13061 lgsval 14858 lgsval4 14874 lgsneg 14878 lgsmod 14880 |
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