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Mirrors > Home > ILE Home > Th. List > pwundifss | Unicode version |
Description: Break up the power class of a union into a union of smaller classes. (Contributed by Jim Kingdon, 30-Sep-2018.) |
Ref | Expression |
---|---|
pwundifss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | undif1ss 3489 | . 2 | |
2 | pwunss 4268 | . . . . 5 | |
3 | unss 3301 | . . . . 5 | |
4 | 2, 3 | mpbir 145 | . . . 4 |
5 | 4 | simpli 110 | . . 3 |
6 | ssequn2 3300 | . . 3 | |
7 | 5, 6 | mpbi 144 | . 2 |
8 | 1, 7 | sseqtri 3181 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1348 cdif 3118 cun 3119 wss 3121 cpw 3566 |
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-un 3125 df-in 3127 df-ss 3134 df-pw 3568 |
This theorem is referenced by: (None) |
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