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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-nn0suc0 | Unicode version |
Description: Constructive proof of a variant of nn0suc 4456. For a constructive proof of nn0suc 4456, see bj-nn0suc 12747. (Contributed by BJ, 19-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-nn0suc0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 2106 |
. . 3
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2 | eqeq1 2106 |
. . . 4
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3 | 2 | rexeqbi1dv 2593 |
. . 3
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4 | 1, 3 | orbi12d 748 |
. 2
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5 | tru 1303 |
. . 3
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6 | a1tru 1315 |
. . . 4
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7 | 6 | rgenw 2446 |
. . 3
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8 | bdeq0 12646 |
. . . . 5
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9 | bdeqsuc 12660 |
. . . . . 6
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10 | 9 | ax-bdex 12598 |
. . . . 5
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11 | 8, 10 | ax-bdor 12595 |
. . . 4
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12 | nfv 1476 |
. . . 4
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13 | orc 674 |
. . . . 5
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14 | 13 | a1d 22 |
. . . 4
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15 | a1tru 1315 |
. . . . 5
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16 | 15 | expi 607 |
. . . 4
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17 | vex 2644 |
. . . . . . . . 9
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18 | 17 | sucid 4277 |
. . . . . . . 8
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19 | eleq2 2163 |
. . . . . . . 8
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20 | 18, 19 | mpbiri 167 |
. . . . . . 7
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21 | suceq 4262 |
. . . . . . . . 9
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22 | 21 | eqeq2d 2111 |
. . . . . . . 8
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23 | 22 | rspcev 2744 |
. . . . . . 7
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24 | 20, 23 | mpancom 416 |
. . . . . 6
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25 | 24 | olcd 694 |
. . . . 5
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26 | 25 | a1d 22 |
. . . 4
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27 | 11, 12, 12, 12, 14, 16, 26 | bj-bdfindis 12730 |
. . 3
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28 | 5, 7, 27 | mp2an 420 |
. 2
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29 | 4, 28 | vtoclri 2716 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 584 ax-in2 585 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-13 1459 ax-14 1460 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-nul 3994 ax-pr 4069 ax-un 4293 ax-bd0 12592 ax-bdim 12593 ax-bdan 12594 ax-bdor 12595 ax-bdn 12596 ax-bdal 12597 ax-bdex 12598 ax-bdeq 12599 ax-bdel 12600 ax-bdsb 12601 ax-bdsep 12663 ax-infvn 12724 |
This theorem depends on definitions: df-bi 116 df-tru 1302 df-fal 1305 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-ral 2380 df-rex 2381 df-rab 2384 df-v 2643 df-dif 3023 df-un 3025 df-in 3027 df-ss 3034 df-nul 3311 df-sn 3480 df-pr 3481 df-uni 3684 df-int 3719 df-suc 4231 df-iom 4443 df-bdc 12620 df-bj-ind 12710 |
This theorem is referenced by: bj-nn0suc 12747 |
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