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Mirrors > Home > MPE Home > Th. List > unipr | Structured version 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 1661 |
. . . 4
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2 | vex 3071 |
. . . . . . . 8
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3 | 2 | elpr 3993 |
. . . . . . 7
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4 | 3 | anbi2i 694 |
. . . . . 6
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5 | andi 862 |
. . . . . 6
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6 | 4, 5 | bitri 249 |
. . . . 5
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7 | 6 | exbii 1635 |
. . . 4
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8 | unipr.1 |
. . . . . . 7
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9 | 8 | clel3 3195 |
. . . . . 6
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10 | exancom 1639 |
. . . . . 6
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11 | 9, 10 | bitri 249 |
. . . . 5
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12 | unipr.2 |
. . . . . . 7
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13 | 12 | clel3 3195 |
. . . . . 6
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14 | exancom 1639 |
. . . . . 6
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15 | 13, 14 | bitri 249 |
. . . . 5
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16 | 11, 15 | orbi12i 521 |
. . . 4
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17 | 1, 7, 16 | 3bitr4ri 278 |
. . 3
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18 | 17 | abbii 2585 |
. 2
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19 | df-un 3431 |
. 2
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20 | df-uni 4190 |
. 2
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21 | 18, 19, 20 | 3eqtr4ri 2491 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-v 3070 df-un 3431 df-sn 3976 df-pr 3978 df-uni 4190 |
This theorem is referenced by: uniprg 4203 unisn 4204 uniintsn 4263 uniop 4692 unex 6478 rankxplim 8187 mrcun 14662 indistps 18731 indistps2 18732 leordtval2 18932 ex-uni 23768 |
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