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Mirrors > Home > ILE Home > Th. List > seqeq2d | 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 |
---|---|
seqeq2d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | seqeqd.1 |
. 2
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2 | seqeq2 10432 |
. 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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-opab 4062 df-mpt 4063 df-cnv 4631 df-dm 4633 df-rn 4634 df-res 4635 df-iota 5174 df-fv 5220 df-ov 5872 df-oprab 5873 df-mpo 5874 df-recs 6300 df-frec 6386 df-seqfrec 10429 |
This theorem is referenced by: seqeq123d 10437 mulgfvalg 12871 |
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