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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 4292 | . 2 | |
2 | ordelss 4296 | . . 3 | |
3 | 2 | ex 114 | . 2 |
4 | 1, 3 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1480 wss 3066 word 4279 con0 4280 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-in 3072 df-ss 3079 df-uni 3732 df-tr 4022 df-iord 4283 df-on 4285 |
This theorem is referenced by: onelssi 4346 ssorduni 4398 onsucelsucr 4419 tfisi 4496 tfrlem9 6209 nntri2or2 6387 phpelm 6753 ennnfonelemk 11902 |
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