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Mirrors > Home > ILE Home > Th. List > xp2dju | Unicode version |
Description: Two times a cardinal number. Exercise 4.56(g) of [Mendelson] p. 258. (Contributed by NM, 27-Sep-2004.) (Revised by Mario Carneiro, 29-Apr-2015.) |
Ref | Expression |
---|---|
xp2dju | ⊔ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpundir 4655 | . 2 | |
2 | df2o3 6389 | . . . 4 | |
3 | df-pr 3577 | . . . 4 | |
4 | 2, 3 | eqtri 2185 | . . 3 |
5 | 4 | xpeq1i 4618 | . 2 |
6 | df-dju 6994 | . 2 ⊔ | |
7 | 1, 5, 6 | 3eqtr4i 2195 | 1 ⊔ |
Colors of variables: wff set class |
Syntax hints: wceq 1342 cun 3109 c0 3404 csn 3570 cpr 3571 cxp 4596 c1o 6368 c2o 6369 ⊔ cdju 6993 |
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-in1 604 ax-in2 605 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 2723 df-dif 3113 df-un 3115 df-nul 3405 df-pr 3577 df-opab 4038 df-suc 4343 df-xp 4604 df-1o 6375 df-2o 6376 df-dju 6994 |
This theorem is referenced by: (None) |
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