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Mirrors > Home > MPE Home > Th. List > unopn | Structured version Unicode version |
Description: The union of two open sets is open. (Contributed by Jeff Madsen, 2-Sep-2009.) |
Ref | Expression |
---|---|
unopn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uniprg 4216 |
. . 3
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2 | 1 | 3adant1 1006 |
. 2
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3 | prssi 4140 |
. . . 4
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4 | uniopn 18652 |
. . . 4
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5 | 3, 4 | sylan2 474 |
. . 3
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6 | 5 | 3impb 1184 |
. 2
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7 | 2, 6 | eqeltrrd 2543 |
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 1955 ax-ext 2432 ax-sep 4524 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-ral 2804 df-rex 2805 df-v 3080 df-un 3444 df-in 3446 df-ss 3453 df-pw 3973 df-sn 3989 df-pr 3991 df-uni 4203 df-top 18645 |
This theorem is referenced by: txcld 19318 icccld 20488 comppfsc 28750 |
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