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Mirrors > Home > NFE Home > Th. List > unopab | Unicode version |
Description: Union of two ordered pair class abstractions. (Contributed by NM, 30-Sep-2002.) |
Ref | Expression |
---|---|
unopab |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unab 3522 |
. . 3
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2 | 19.43 1605 |
. . . . 5
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3 | andi 837 |
. . . . . . . 8
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4 | 3 | exbii 1582 |
. . . . . . 7
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5 | 19.43 1605 |
. . . . . . 7
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6 | 4, 5 | bitr2i 241 |
. . . . . 6
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7 | 6 | exbii 1582 |
. . . . 5
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8 | 2, 7 | bitr3i 242 |
. . . 4
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9 | 8 | abbii 2466 |
. . 3
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10 | 1, 9 | eqtri 2373 |
. 2
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11 | df-opab 4624 |
. . 3
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12 | df-opab 4624 |
. . 3
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13 | 11, 12 | uneq12i 3417 |
. 2
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14 | df-opab 4624 |
. 2
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15 | 10, 13, 14 | 3eqtr4i 2383 |
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-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2479 df-v 2862 df-nin 3212 df-compl 3213 df-un 3215 df-opab 4624 |
This theorem is referenced by: xpundi 4833 xpundir 4834 cnvun 5034 coundi 5083 coundir 5084 |
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