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Mirrors > Home > NFE Home > Th. List > reuun2 | Unicode version |
Description: Transfer uniqueness to a smaller or larger class. (Contributed by NM, 21-Oct-2005.) |
Ref | Expression |
---|---|
reuun2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2621 |
. . 3
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2 | euor2 2272 |
. . 3
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3 | 1, 2 | sylnbi 297 |
. 2
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4 | df-reu 2622 |
. . 3
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5 | elun 3221 |
. . . . . 6
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6 | 5 | anbi1i 676 |
. . . . 5
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7 | andir 838 |
. . . . . 6
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8 | orcom 376 |
. . . . . 6
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9 | 7, 8 | bitri 240 |
. . . . 5
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10 | 6, 9 | bitri 240 |
. . . 4
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11 | 10 | eubii 2213 |
. . 3
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12 | 4, 11 | bitri 240 |
. 2
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13 | df-reu 2622 |
. 2
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14 | 3, 12, 13 | 3bitr4g 279 |
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 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2479 df-rex 2621 df-reu 2622 df-v 2862 df-nin 3212 df-compl 3213 df-un 3215 |
This theorem is referenced by: (None) |
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