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Mirrors > Home > NFE Home > Th. List > iuncom4 | Unicode version |
Description: Commutation of union with indexed union. (Contributed by Mario Carneiro, 18-Jan-2014.) |
Ref | Expression |
---|---|
iuncom4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2621 |
. . . . . . 7
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2 | 1 | rexbii 2640 |
. . . . . 6
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3 | rexcom4 2879 |
. . . . . 6
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4 | 2, 3 | bitri 240 |
. . . . 5
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5 | r19.41v 2765 |
. . . . . 6
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6 | 5 | exbii 1582 |
. . . . 5
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7 | 4, 6 | bitri 240 |
. . . 4
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8 | eluni2 3896 |
. . . . 5
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9 | 8 | rexbii 2640 |
. . . 4
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10 | df-rex 2621 |
. . . . 5
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11 | eliun 3974 |
. . . . . . 7
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12 | 11 | anbi1i 676 |
. . . . . 6
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13 | 12 | exbii 1582 |
. . . . 5
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14 | 10, 13 | bitri 240 |
. . . 4
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15 | 7, 9, 14 | 3bitr4i 268 |
. . 3
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16 | eliun 3974 |
. . 3
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17 | eluni2 3896 |
. . 3
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18 | 15, 16, 17 | 3bitr4i 268 |
. 2
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19 | 18 | eqriv 2350 |
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-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2479 df-ral 2620 df-rex 2621 df-v 2862 df-uni 3893 df-iun 3972 |
This theorem is referenced by: (None) |
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