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Mirrors > Home > ILE Home > Th. List > recseq | Unicode version |
Description: Equality theorem for recs. (Contributed by Stefan O'Rear, 18-Jan-2015.) |
Ref | Expression |
---|---|
recseq |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveq1 5428 |
. . . . . . . 8
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2 | 1 | eqeq2d 2152 |
. . . . . . 7
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3 | 2 | ralbidv 2438 |
. . . . . 6
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4 | 3 | anbi2d 460 |
. . . . 5
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5 | 4 | rexbidv 2439 |
. . . 4
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6 | 5 | abbidv 2258 |
. . 3
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7 | 6 | unieqd 3755 |
. 2
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8 | df-recs 6210 |
. 2
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9 | df-recs 6210 |
. 2
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10 | 7, 8, 9 | 3eqtr4g 2198 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-uni 3745 df-br 3938 df-iota 5096 df-fv 5139 df-recs 6210 |
This theorem is referenced by: rdgeq1 6276 rdgeq2 6277 freceq1 6297 freceq2 6298 frecsuclem 6311 |
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