Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > onun2 | Unicode version |
Description: The union of two ordinal numbers is an ordinal number. (Contributed by Jim Kingdon, 25-Jul-2019.) |
Ref | Expression |
---|---|
onun2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prssi 3543 | . 2 | |
2 | prexg 3966 | . . . 4 | |
3 | ssonuni 4232 | . . . 4 | |
4 | 2, 3 | syl 14 | . . 3 |
5 | uniprg 3616 | . . . 4 | |
6 | 5 | eleq1d 2147 | . . 3 |
7 | 4, 6 | sylibd 147 | . 2 |
8 | 1, 7 | mpd 13 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wcel 1433 cvv 2601 cun 2971 wss 2973 cpr 3399 cuni 3601 con0 4118 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pr 3964 ax-un 4188 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-sn 3404 df-pr 3405 df-uni 3602 df-tr 3876 df-iord 4121 df-on 4123 |
This theorem is referenced by: onun2i 4235 rdgon 5996 |
Copyright terms: Public domain | W3C validator |