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Mirrors > Home > MPE Home > Th. List > uniprg | Structured version Visualization 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, 25-Aug-2006.) |
Ref | Expression |
---|---|
uniprg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | preq1 4042 |
. . . 4
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2 | 1 | unieqd 4200 |
. . 3
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3 | uneq1 3572 |
. . 3
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4 | 2, 3 | eqeq12d 2486 |
. 2
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5 | preq2 4043 |
. . . 4
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6 | 5 | unieqd 4200 |
. . 3
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7 | uneq2 3573 |
. . 3
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8 | 6, 7 | eqeq12d 2486 |
. 2
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9 | vex 3034 |
. . 3
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10 | vex 3034 |
. . 3
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11 | 9, 10 | unipr 4203 |
. 2
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12 | 4, 8, 11 | vtocl2g 3097 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-rex 2762 df-v 3033 df-un 3395 df-sn 3960 df-pr 3962 df-uni 4191 |
This theorem is referenced by: wunun 9153 tskun 9229 gruun 9249 mrcun 15606 unopn 20010 indistopon 20093 uncon 20521 limcun 22929 sshjval3 27088 prsiga 29027 unelsiga 29030 unelldsys 29054 measxun2 29106 measssd 29111 carsgsigalem 29220 carsgclctun 29226 pmeasmono 29230 probun 29325 indispcon 30029 kelac2 35994 fourierdlem70 38152 fourierdlem71 38153 saluncl 38290 prsal 38291 meadjun 38416 omeunle 38456 |
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