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Mirrors > Home > ILE Home > Th. List > rdgeq1 | Unicode version |
Description: Equality theorem for the recursive definition generator. (Contributed by NM, 9-Apr-1995.) (Revised by Mario Carneiro, 9-May-2015.) |
Ref | Expression |
---|---|
rdgeq1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveq1 5514 |
. . . . . 6
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2 | 1 | iuneq2d 3911 |
. . . . 5
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3 | 2 | uneq2d 3289 |
. . . 4
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4 | 3 | mpteq2dv 4094 |
. . 3
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5 | recseq 6306 |
. . 3
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6 | 4, 5 | syl 14 |
. 2
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7 | df-irdg 6370 |
. 2
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8 | df-irdg 6370 |
. 2
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9 | 6, 7, 8 | 3eqtr4g 2235 |
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-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-uni 3810 df-iun 3888 df-br 4004 df-opab 4065 df-mpt 4066 df-iota 5178 df-fv 5224 df-recs 6305 df-irdg 6370 |
This theorem is referenced by: omv 6455 oeiv 6456 |
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