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Mirrors > Home > MPE Home > Th. List > rdgsucmptf | Structured version Visualization version Unicode version |
Description: The value of the recursive definition generator at a successor (special case where the characteristic function uses the map operation). (Contributed by NM, 22-Oct-2003.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
rdgsucmptf.1 |
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rdgsucmptf.2 |
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rdgsucmptf.3 |
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rdgsucmptf.4 |
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rdgsucmptf.5 |
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Ref | Expression |
---|---|
rdgsucmptf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rdgsuc 7147 |
. . 3
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2 | rdgsucmptf.4 |
. . . 4
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3 | 2 | fveq1i 5871 |
. . 3
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4 | 2 | fveq1i 5871 |
. . . 4
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5 | 4 | fveq2i 5873 |
. . 3
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6 | 1, 3, 5 | 3eqtr4g 2512 |
. 2
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7 | fvex 5880 |
. . 3
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8 | nfmpt1 4495 |
. . . . . . 7
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9 | rdgsucmptf.1 |
. . . . . . 7
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10 | 8, 9 | nfrdg 7137 |
. . . . . 6
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11 | 2, 10 | nfcxfr 2592 |
. . . . 5
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12 | rdgsucmptf.2 |
. . . . 5
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13 | 11, 12 | nffv 5877 |
. . . 4
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14 | rdgsucmptf.3 |
. . . 4
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15 | rdgsucmptf.5 |
. . . 4
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16 | eqid 2453 |
. . . 4
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17 | 13, 14, 15, 16 | fvmptf 5971 |
. . 3
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18 | 7, 17 | mpan 677 |
. 2
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19 | 6, 18 | sylan9eq 2507 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1671 ax-4 1684 ax-5 1760 ax-6 1807 ax-7 1853 ax-8 1891 ax-9 1898 ax-10 1917 ax-11 1922 ax-12 1935 ax-13 2093 ax-ext 2433 ax-rep 4518 ax-sep 4528 ax-nul 4537 ax-pow 4584 ax-pr 4642 ax-un 6588 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3or 987 df-3an 988 df-tru 1449 df-ex 1666 df-nf 1670 df-sb 1800 df-eu 2305 df-mo 2306 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2583 df-ne 2626 df-ral 2744 df-rex 2745 df-reu 2746 df-rab 2748 df-v 3049 df-sbc 3270 df-csb 3366 df-dif 3409 df-un 3411 df-in 3413 df-ss 3420 df-pss 3422 df-nul 3734 df-if 3884 df-pw 3955 df-sn 3971 df-pr 3973 df-tp 3975 df-op 3977 df-uni 4202 df-iun 4283 df-br 4406 df-opab 4465 df-mpt 4466 df-tr 4501 df-eprel 4748 df-id 4752 df-po 4758 df-so 4759 df-fr 4796 df-we 4798 df-xp 4843 df-rel 4844 df-cnv 4845 df-co 4846 df-dm 4847 df-rn 4848 df-res 4849 df-ima 4850 df-pred 5383 df-ord 5429 df-on 5430 df-lim 5431 df-suc 5432 df-iota 5549 df-fun 5587 df-fn 5588 df-f 5589 df-f1 5590 df-fo 5591 df-f1o 5592 df-fv 5593 df-wrecs 7033 df-recs 7095 df-rdg 7133 |
This theorem is referenced by: rdgsucmpt2 7153 rdgsucmpt 7154 |
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