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Mirrors > Home > MPE Home > Th. List > pwundif | Structured version Unicode version |
Description: Break up the power class of a union into a union of smaller classes. (Contributed by NM, 25-Mar-2007.) (Proof shortened by Thierry Arnoux, 20-Dec-2016.) |
Ref | Expression |
---|---|
pwundif |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | undif1 3865 |
. 2
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2 | pwunss 4737 |
. . . . 5
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3 | unss 3641 |
. . . . 5
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4 | 2, 3 | mpbir 209 |
. . . 4
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5 | 4 | simpli 458 |
. . 3
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6 | ssequn2 3640 |
. . 3
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7 | 5, 6 | mpbi 208 |
. 2
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8 | 1, 7 | eqtr2i 2484 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-ne 2650 df-ral 2804 df-rab 2808 df-v 3080 df-dif 3442 df-un 3444 df-in 3446 df-ss 3453 df-nul 3749 df-pw 3973 |
This theorem is referenced by: pwfilem 7719 |
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