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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssun1 3281 | . 2 | |
2 | df-suc 4344 | . 2 | |
3 | 1, 2 | sseqtrri 3173 | 1 |
Colors of variables: wff set class |
Syntax hints: cun 3110 wss 3112 csn 3571 csuc 4338 |
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-v 2724 df-un 3116 df-in 3118 df-ss 3125 df-suc 4344 |
This theorem is referenced by: trsuc 4395 ordsuc 4535 0elnn 4591 sucinc 6405 sucinc2 6406 oasuc 6424 phplem4 6813 phplem4dom 6820 phplem4on 6825 fiintim 6886 fidcenumlemrk 6911 fidcenumlemr 6912 bj-nntrans 13685 |
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