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Mirrors > Home > MPE Home > Th. List > coundir | Structured version Visualization version Unicode version |
Description: Class composition distributes over union. (Contributed by NM, 21-Dec-2008.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
coundir |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unopab 4477 |
. . 3
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2 | brun 4450 |
. . . . . . . 8
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3 | 2 | anbi2i 699 |
. . . . . . 7
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4 | andi 877 |
. . . . . . 7
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5 | 3, 4 | bitri 253 |
. . . . . 6
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6 | 5 | exbii 1717 |
. . . . 5
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7 | 19.43 1744 |
. . . . 5
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8 | 6, 7 | bitr2i 254 |
. . . 4
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9 | 8 | opabbii 4466 |
. . 3
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10 | 1, 9 | eqtri 2472 |
. 2
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11 | df-co 4842 |
. . 3
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12 | df-co 4842 |
. . 3
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13 | 11, 12 | uneq12i 3585 |
. 2
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14 | df-co 4842 |
. 2
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15 | 10, 13, 14 | 3eqtr4ri 2483 |
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 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-tru 1446 df-ex 1663 df-nf 1667 df-sb 1797 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2580 df-v 3046 df-un 3408 df-br 4402 df-opab 4461 df-co 4842 |
This theorem is referenced by: diophrw 35595 diophren 35650 rtrclex 36218 trclubgNEW 36219 trclexi 36221 rtrclexi 36222 cnvtrcl0 36227 trrelsuperrel2dg 36257 |
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