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Mirrors > Home > MPE Home > Th. List > ssundif | Structured version Visualization version Unicode version |
Description: A condition equivalent to inclusion in the union of two classes. (Contributed by NM, 26-Mar-2007.) |
Ref | Expression |
---|---|
ssundif |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm5.6 924 |
. . . 4
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2 | eldif 3416 |
. . . . 5
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3 | 2 | imbi1i 327 |
. . . 4
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4 | elun 3576 |
. . . . 5
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5 | 4 | imbi2i 314 |
. . . 4
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6 | 1, 3, 5 | 3bitr4ri 282 |
. . 3
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7 | 6 | albii 1693 |
. 2
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8 | dfss2 3423 |
. 2
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9 | dfss2 3423 |
. 2
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10 | 7, 8, 9 | 3bitr4i 281 |
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 1671 ax-4 1684 ax-5 1760 ax-6 1807 ax-7 1853 ax-10 1917 ax-11 1922 ax-12 1935 ax-13 2093 ax-ext 2433 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-tru 1449 df-ex 1666 df-nf 1670 df-sb 1800 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2583 df-v 3049 df-dif 3409 df-un 3411 df-in 3413 df-ss 3420 |
This theorem is referenced by: difcom 3854 uneqdifeq 3858 ssunsn2 4134 elpwun 6609 soex 6741 ressuppssdif 6941 frfi 7821 cantnfp1lem3 8190 dfacfin7 8834 zornn0g 8940 fpwwe2lem13 9072 hashbclem 12622 incexclem 13906 ramub1lem1 14996 lpcls 20392 cmpcld 20429 alexsubALTlem3 21076 restmetu 21597 uniiccdif 22547 abelthlem2 23399 abelthlem3 23400 imadifss 31940 frege124d 36365 |
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