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Mirrors > Home > MPE Home > Th. List > intnex | Structured version Visualization version Unicode version |
Description: If a class intersection is not a set, it must be the universe. (Contributed by NM, 3-Jul-2005.) |
Ref | Expression |
---|---|
intnex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | intex 4557 |
. . . 4
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2 | 1 | necon1bbii 2692 |
. . 3
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3 | inteq 4229 |
. . . 4
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4 | int0 4240 |
. . . 4
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5 | 3, 4 | syl6eq 2521 |
. . 3
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6 | 2, 5 | sylbi 200 |
. 2
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7 | vprc 4534 |
. . 3
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8 | eleq1 2537 |
. . 3
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9 | 7, 8 | mtbiri 310 |
. 2
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10 | 6, 9 | impbii 192 |
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-8 1906 ax-9 1913 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 ax-sep 4518 |
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-ne 2643 df-ral 2761 df-v 3033 df-dif 3393 df-in 3397 df-ss 3404 df-nul 3723 df-int 4227 |
This theorem is referenced by: intabs 4562 relintabex 36258 |
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