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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-indsuc | Unicode version |
Description: A direct consequence of the definition of Ind. (Contributed by BJ, 30-Nov-2019.) |
Ref | Expression |
---|---|
bj-indsuc | Ind |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-bj-ind 13702 | . . 3 Ind | |
2 | 1 | simprbi 273 | . 2 Ind |
3 | suceq 4377 | . . . 4 | |
4 | 3 | eleq1d 2233 | . . 3 |
5 | 4 | rspcv 2824 | . 2 |
6 | 2, 5 | syl5com 29 | 1 Ind |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1342 wcel 2135 wral 2442 c0 3407 csuc 4340 Ind wind 13701 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-v 2726 df-un 3118 df-sn 3579 df-suc 4346 df-bj-ind 13702 |
This theorem is referenced by: bj-indint 13706 bj-peano2 13714 bj-inf2vnlem2 13746 |
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