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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-nn0suc0 | Unicode version |
Description: Constructive proof of a variant of nn0suc 4615. For a constructive proof of nn0suc 4615, see bj-nn0suc 14987. (Contributed by BJ, 19-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-nn0suc0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 2194 |
. . 3
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2 | eqeq1 2194 |
. . . 4
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3 | 2 | rexeqbi1dv 2692 |
. . 3
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4 | 1, 3 | orbi12d 794 |
. 2
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5 | tru 1367 |
. . 3
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6 | trud 1379 |
. . . 4
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7 | 6 | rgenw 2542 |
. . 3
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8 | bdeq0 14890 |
. . . . 5
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9 | bdeqsuc 14904 |
. . . . . 6
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10 | 9 | ax-bdex 14842 |
. . . . 5
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11 | 8, 10 | ax-bdor 14839 |
. . . 4
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12 | nfv 1538 |
. . . 4
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13 | orc 713 |
. . . . 5
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14 | 13 | a1d 22 |
. . . 4
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15 | trud 1379 |
. . . . 5
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16 | 15 | expi 639 |
. . . 4
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17 | vex 2752 |
. . . . . . . . 9
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18 | 17 | sucid 4429 |
. . . . . . . 8
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19 | eleq2 2251 |
. . . . . . . 8
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20 | 18, 19 | mpbiri 168 |
. . . . . . 7
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21 | suceq 4414 |
. . . . . . . . 9
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22 | 21 | eqeq2d 2199 |
. . . . . . . 8
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23 | 22 | rspcev 2853 |
. . . . . . 7
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24 | 20, 23 | mpancom 422 |
. . . . . 6
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25 | 24 | olcd 735 |
. . . . 5
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26 | 25 | a1d 22 |
. . . 4
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27 | 11, 12, 12, 12, 14, 16, 26 | bj-bdfindis 14970 |
. . 3
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28 | 5, 7, 27 | mp2an 426 |
. 2
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29 | 4, 28 | vtoclri 2824 |
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-in1 615 ax-in2 616 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-13 2160 ax-14 2161 ax-ext 2169 ax-nul 4141 ax-pr 4221 ax-un 4445 ax-bd0 14836 ax-bdim 14837 ax-bdan 14838 ax-bdor 14839 ax-bdn 14840 ax-bdal 14841 ax-bdex 14842 ax-bdeq 14843 ax-bdel 14844 ax-bdsb 14845 ax-bdsep 14907 ax-infvn 14964 |
This theorem depends on definitions: df-bi 117 df-tru 1366 df-fal 1369 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ral 2470 df-rex 2471 df-rab 2474 df-v 2751 df-dif 3143 df-un 3145 df-in 3147 df-ss 3154 df-nul 3435 df-sn 3610 df-pr 3611 df-uni 3822 df-int 3857 df-suc 4383 df-iom 4602 df-bdc 14864 df-bj-ind 14950 |
This theorem is referenced by: bj-nn0suc 14987 |
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