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Mirrors > Home > ILE Home > Th. List > unss | Unicode version |
Description: The union of two subclasses is a subclass. Theorem 27 of [Suppes] p. 27 and its converse. (Contributed by NM, 11-Jun-2004.) |
Ref | Expression |
---|---|
unss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfss2 3091 |
. 2
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2 | 19.26 1458 |
. . 3
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3 | elun 3222 |
. . . . . 6
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4 | 3 | imbi1i 237 |
. . . . 5
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5 | jaob 700 |
. . . . 5
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6 | 4, 5 | bitri 183 |
. . . 4
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7 | 6 | albii 1447 |
. . 3
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8 | dfss2 3091 |
. . . 4
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9 | dfss2 3091 |
. . . 4
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10 | 8, 9 | anbi12i 456 |
. . 3
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11 | 2, 7, 10 | 3bitr4i 211 |
. 2
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12 | 1, 11 | bitr2i 184 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 |
This theorem is referenced by: unssi 3256 unssd 3257 unssad 3258 unssbd 3259 uneqin 3332 undifss 3448 prss 3684 prssg 3685 tpss 3693 pwundifss 4215 ordsucss 4428 elnn 4527 eqrelrel 4648 xpsspw 4659 relun 4664 relcoi2 5077 dfer2 6438 fimaxre2 11030 uncld 12321 bdeqsuc 13250 exmid1stab 13368 |
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