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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 4434 |
. 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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-un 3148 df-sn 3613 df-suc 4389 |
This theorem is referenced by: eqelsuc 4437 unon 4528 ordunisuc2r 4531 ordsoexmid 4579 limom 4631 0elnn 4636 tfrexlem 6360 tfri1dALT 6377 tfrcl 6390 frecabcl 6425 phplem4 6884 fiintim 6958 fidcenumlemr 6985 nninfwlpoimlemginf 7205 pw1ne3 7260 sucpw1ne3 7262 sucpw1nel3 7263 prarloclemarch2 7449 prarloclemlt 7523 ennnfonelemex 12468 ennnfonelemrn 12473 bj-nn0suc0 15180 bj-nnelirr 15183 bj-inf2vnlem2 15201 bj-findis 15209 nninfsellemeq 15242 |
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