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Mirrors > Home > ILE Home > Th. List > uniprg | Unicode version |
Description: The union of a pair is the union of its members. Proposition 5.7 of [TakeutiZaring] p. 16. (Contributed by NM, 25-Aug-2006.) |
Ref | Expression |
---|---|
uniprg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | preq1 3438 |
. . . 4
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2 | 1 | unieqd 3582 |
. . 3
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3 | uneq1 3084 |
. . 3
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4 | 2, 3 | eqeq12d 2051 |
. 2
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5 | preq2 3439 |
. . . 4
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6 | 5 | unieqd 3582 |
. . 3
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7 | uneq2 3085 |
. . 3
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8 | 6, 7 | eqeq12d 2051 |
. 2
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9 | vex 2554 |
. . 3
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10 | vex 2554 |
. . 3
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11 | 9, 10 | unipr 3585 |
. 2
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12 | 4, 8, 11 | vtocl2g 2611 |
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 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-rex 2306 df-v 2553 df-un 2916 df-sn 3373 df-pr 3374 df-uni 3572 |
This theorem is referenced by: onun2 4182 |
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