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Mirrors > Home > ILE Home > Th. List > sucid | Unicode version |
Description: A set belongs to its successor. (Contributed by NM, 22-Jun-1994.) (Proof shortened by Alan Sare, 18-Feb-2012.) (Proof shortened by Scott Fenton, 20-Feb-2012.) |
Ref | Expression |
---|---|
sucid.1 |
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Ref | Expression |
---|---|
sucid |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sucid.1 |
. 2
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2 | sucidg 4412 |
. 2
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3 | 1, 2 | ax-mp 5 |
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-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-un 3133 df-sn 3597 df-suc 4367 |
This theorem is referenced by: eqelsuc 4415 unon 4506 ordunisuc2r 4509 ordsoexmid 4557 limom 4609 0elnn 4614 tfrexlem 6328 tfri1dALT 6345 tfrcl 6358 frecabcl 6393 phplem4 6848 fiintim 6921 fidcenumlemr 6947 nninfwlpoimlemginf 7167 pw1ne3 7222 sucpw1ne3 7224 sucpw1nel3 7225 prarloclemarch2 7396 prarloclemlt 7470 ennnfonelemex 12385 ennnfonelemrn 12390 bj-nn0suc0 14324 bj-nnelirr 14327 bj-inf2vnlem2 14345 bj-findis 14353 nninfsellemeq 14386 |
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