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Mirrors > Home > ILE Home > Th. List > unidif0 | Unicode version |
Description: The removal of the empty set from a class does not affect its union. (Contributed by NM, 22-Mar-2004.) |
Ref | Expression |
---|---|
unidif0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | n0i 3409 | . . . . . . 7 | |
2 | 1 | pm4.71i 389 | . . . . . 6 |
3 | 2 | anbi1i 454 | . . . . 5 |
4 | an32 552 | . . . . 5 | |
5 | anass 399 | . . . . 5 | |
6 | 3, 4, 5 | 3bitr2ri 208 | . . . 4 |
7 | 6 | exbii 1592 | . . 3 |
8 | eluni 3786 | . . . 4 | |
9 | eldif 3120 | . . . . . . 7 | |
10 | velsn 3587 | . . . . . . . . 9 | |
11 | 10 | notbii 658 | . . . . . . . 8 |
12 | 11 | anbi2i 453 | . . . . . . 7 |
13 | 9, 12 | bitri 183 | . . . . . 6 |
14 | 13 | anbi2i 453 | . . . . 5 |
15 | 14 | exbii 1592 | . . . 4 |
16 | 8, 15 | bitri 183 | . . 3 |
17 | eluni 3786 | . . 3 | |
18 | 7, 16, 17 | 3bitr4i 211 | . 2 |
19 | 18 | eqriv 2161 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 103 wceq 1342 wex 1479 wcel 2135 cdif 3108 c0 3404 csn 3570 cuni 3783 |
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-nul 3405 df-sn 3576 df-uni 3784 |
This theorem is referenced by: (None) |
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