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Mirrors > Home > ILE Home > Th. List > unipr | Unicode version |
Description: The union of a pair is the union of its members. Proposition 5.7 of [TakeutiZaring] p. 16. (Contributed by NM, 23-Aug-1993.) |
Ref | Expression |
---|---|
unipr.1 |
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unipr.2 |
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Ref | Expression |
---|---|
unipr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.43 1628 |
. . . 4
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2 | vex 2740 |
. . . . . . . 8
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3 | 2 | elpr 3613 |
. . . . . . 7
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4 | 3 | anbi2i 457 |
. . . . . 6
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5 | andi 818 |
. . . . . 6
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6 | 4, 5 | bitri 184 |
. . . . 5
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7 | 6 | exbii 1605 |
. . . 4
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8 | unipr.1 |
. . . . . . 7
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9 | 8 | clel3 2872 |
. . . . . 6
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10 | exancom 1608 |
. . . . . 6
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11 | 9, 10 | bitri 184 |
. . . . 5
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12 | unipr.2 |
. . . . . . 7
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13 | 12 | clel3 2872 |
. . . . . 6
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14 | exancom 1608 |
. . . . . 6
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15 | 13, 14 | bitri 184 |
. . . . 5
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16 | 11, 15 | orbi12i 764 |
. . . 4
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17 | 1, 7, 16 | 3bitr4ri 213 |
. . 3
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18 | 17 | abbii 2293 |
. 2
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19 | df-un 3133 |
. 2
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20 | df-uni 3810 |
. 2
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21 | 18, 19, 20 | 3eqtr4ri 2209 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-un 3133 df-sn 3598 df-pr 3599 df-uni 3810 |
This theorem is referenced by: uniprg 3824 unisn 3825 uniop 4255 unex 4441 bj-unex 14641 |
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