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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 5252 |
. . . . . 6
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2 | 1 | iuneq2d 3729 |
. . . . 5
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3 | 2 | uneq2d 3138 |
. . . 4
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4 | 3 | mpteq2dv 3895 |
. . 3
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5 | recseq 6003 |
. . 3
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6 | 4, 5 | syl 14 |
. 2
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7 | df-irdg 6067 |
. 2
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8 | df-irdg 6067 |
. 2
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9 | 6, 7, 8 | 3eqtr4g 2140 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 |
This theorem depends on definitions: df-bi 115 df-tru 1288 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-ral 2358 df-rex 2359 df-v 2614 df-un 2988 df-in 2990 df-ss 2997 df-uni 3628 df-iun 3706 df-br 3812 df-opab 3866 df-mpt 3867 df-iota 4934 df-fv 4977 df-recs 6002 df-irdg 6067 |
This theorem is referenced by: omv 6148 oeiv 6149 |
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