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Mirrors > Home > ILE Home > Th. List > sssucid | Unicode version |
Description: A class is included in its own successor. Part of Proposition 7.23 of [TakeutiZaring] p. 41 (generalized to arbitrary classes). (Contributed by NM, 31-May-1994.) |
Ref | Expression |
---|---|
sssucid |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssun1 3313 |
. 2
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2 | df-suc 4389 |
. 2
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3 | 1, 2 | sseqtrri 3205 |
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-in 3150 df-ss 3157 df-suc 4389 |
This theorem is referenced by: trsuc 4440 ordsuc 4580 0elnn 4636 sucinc 6471 sucinc2 6472 oasuc 6490 phplem4 6884 phplem4dom 6891 phplem4on 6896 fiintim 6958 fidcenumlemrk 6984 fidcenumlemr 6985 bj-nntrans 15181 |
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