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Mirrors > Home > MPE Home > Th. List > unss | Structured version Visualization version 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 3421 |
. 2
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2 | 19.26 1732 |
. . 3
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3 | elun 3574 |
. . . . . 6
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4 | 3 | imbi1i 327 |
. . . . 5
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5 | jaob 792 |
. . . . 5
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6 | 4, 5 | bitri 253 |
. . . 4
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7 | 6 | albii 1691 |
. . 3
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8 | dfss2 3421 |
. . . 4
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9 | dfss2 3421 |
. . . 4
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10 | 8, 9 | anbi12i 703 |
. . 3
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11 | 2, 7, 10 | 3bitr4i 281 |
. 2
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12 | 1, 11 | bitr2i 254 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-v 3047 df-un 3409 df-in 3411 df-ss 3418 |
This theorem is referenced by: unssi 3609 unssd 3610 unssad 3611 unssbd 3612 nsspssun 3676 uneqin 3694 uneqdifeq 3856 prss 4126 prssg 4127 ssunsn2 4131 tpss 4137 pwundif 4741 eqrelrel 4936 xpsspw 4948 relun 4950 relcoi2 5363 fnsuppres 6942 wfrlem15 7050 dfer2 7364 isinf 7785 fiin 7936 trcl 8212 supxrun 11601 trclun 13078 isumltss 13906 rpnnen2 14278 lcmfunsnlem 14614 lcmfun 14618 coprmprod 14678 coprmproddvdslem 14679 lubun 16369 isipodrs 16407 fpwipodrs 16410 ipodrsima 16411 aspval2 18571 unocv 19243 uncld 20056 restntr 20198 cmpcld 20417 uncmp 20418 ufprim 20924 tsmsfbas 21142 ovolctb2 22445 ovolun 22452 unmbl 22491 plyun0 23151 sshjcl 27008 sshjval2 27064 shlub 27067 ssjo 27100 spanuni 27197 dfon2lem3 30431 dfon2lem7 30435 clsun 30984 mblfinlem3 31979 ismblfin 31981 paddssat 33379 pclunN 33463 paddunN 33492 poldmj1N 33493 pclfinclN 33515 lsmfgcl 35932 ssuncl 36174 sssymdifcl 36176 undmrnresiss 36210 mptrcllem 36220 cnvrcl0 36232 dfrtrcl5 36236 brtrclfv2 36319 unhe1 36381 dffrege76 36535 iunopeqop 39005 |
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