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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 3420 | . . . . . . 7 | |
2 | 1 | pm4.71i 389 | . . . . . 6 |
3 | 2 | anbi1i 455 | . . . . 5 |
4 | an32 557 | . . . . 5 | |
5 | anass 399 | . . . . 5 | |
6 | 3, 4, 5 | 3bitr2ri 208 | . . . 4 |
7 | 6 | exbii 1598 | . . 3 |
8 | eluni 3799 | . . . 4 | |
9 | eldif 3130 | . . . . . . 7 | |
10 | velsn 3600 | . . . . . . . . 9 | |
11 | 10 | notbii 663 | . . . . . . . 8 |
12 | 11 | anbi2i 454 | . . . . . . 7 |
13 | 9, 12 | bitri 183 | . . . . . 6 |
14 | 13 | anbi2i 454 | . . . . 5 |
15 | 14 | exbii 1598 | . . . 4 |
16 | 8, 15 | bitri 183 | . . 3 |
17 | eluni 3799 | . . 3 | |
18 | 7, 16, 17 | 3bitr4i 211 | . 2 |
19 | 18 | eqriv 2167 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 103 wceq 1348 wex 1485 wcel 2141 cdif 3118 c0 3414 csn 3583 cuni 3796 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-dif 3123 df-nul 3415 df-sn 3589 df-uni 3797 |
This theorem is referenced by: (None) |
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