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Mirrors > Home > ILE Home > Th. List > eldifpw | Unicode version |
Description: Membership in a power class difference. (Contributed by NM, 25-Mar-2007.) |
Ref | Expression |
---|---|
eldifpw.1 |
Ref | Expression |
---|---|
eldifpw |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elpwi 3368 | . . . 4 | |
2 | unss1 3112 | . . . . 5 | |
3 | eldifpw.1 | . . . . . . 7 | |
4 | unexg 4178 | . . . . . . 7 | |
5 | 3, 4 | mpan2 401 | . . . . . 6 |
6 | elpwg 3367 | . . . . . 6 | |
7 | 5, 6 | syl 14 | . . . . 5 |
8 | 2, 7 | syl5ibr 145 | . . . 4 |
9 | 1, 8 | mpd 13 | . . 3 |
10 | elpwi 3368 | . . . . 5 | |
11 | 10 | unssbd 3121 | . . . 4 |
12 | 11 | con3i 562 | . . 3 |
13 | 9, 12 | anim12i 321 | . 2 |
14 | eldif 2927 | . 2 | |
15 | 13, 14 | sylibr 137 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wb 98 wcel 1393 cvv 2557 cdif 2914 cun 2915 wss 2917 cpw 3359 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-13 1404 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pr 3944 ax-un 4170 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-v 2559 df-dif 2920 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-uni 3581 |
This theorem is referenced by: (None) |
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