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Mirrors > Home > ILE Home > Th. List > onelss | Unicode version |
Description: An element of an ordinal number is a subset of the number. (Contributed by NM, 5-Jun-1994.) (Proof shortened by Andrew Salmon, 25-Jul-2011.) |
Ref | Expression |
---|---|
onelss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eloni 4347 | . 2 | |
2 | ordelss 4351 | . . 3 | |
3 | 2 | ex 114 | . 2 |
4 | 1, 3 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2135 wss 3111 word 4334 con0 4335 |
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-rex 2448 df-v 2723 df-in 3117 df-ss 3124 df-uni 3784 df-tr 4075 df-iord 4338 df-on 4340 |
This theorem is referenced by: onelssi 4401 ssorduni 4458 onsucelsucr 4479 tfisi 4558 tfrlem9 6278 nntri2or2 6457 phpelm 6823 exmidontri2or 7190 ennnfonelemk 12270 |
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