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Mirrors > Home > ILE Home > Th. List > iunopab | Unicode version |
Description: Move indexed union inside an ordered-pair abstraction. (Contributed by Stefan O'Rear, 20-Feb-2015.) |
Ref | Expression |
---|---|
iunopab |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elopab 4094 |
. . . . 5
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2 | 1 | rexbii 2386 |
. . . 4
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3 | rexcom4 2643 |
. . . . 5
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4 | rexcom4 2643 |
. . . . . . 7
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5 | r19.42v 2525 |
. . . . . . . 8
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6 | 5 | exbii 1542 |
. . . . . . 7
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7 | 4, 6 | bitri 183 |
. . . . . 6
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8 | 7 | exbii 1542 |
. . . . 5
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9 | 3, 8 | bitri 183 |
. . . 4
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10 | 2, 9 | bitri 183 |
. . 3
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11 | 10 | abbii 2204 |
. 2
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12 | df-iun 3738 |
. 2
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13 | df-opab 3906 |
. 2
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14 | 11, 12, 13 | 3eqtr4i 2119 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-14 1451 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3963 ax-pow 4015 ax-pr 4045 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-rex 2366 df-v 2622 df-un 3004 df-in 3006 df-ss 3013 df-pw 3435 df-sn 3456 df-pr 3457 df-op 3459 df-iun 3738 df-opab 3906 |
This theorem is referenced by: (None) |
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