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Mirrors > Home > ILE Home > Th. List > intexr | Unicode version |
Description: If the intersection of a class exists, the class is nonempty. (Contributed by Jim Kingdon, 27-Aug-2018.) |
Ref | Expression |
---|---|
intexr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vprc 3992 |
. . 3
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2 | inteq 3713 |
. . . . 5
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3 | int0 3724 |
. . . . 5
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4 | 2, 3 | syl6eq 2143 |
. . . 4
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5 | 4 | eleq1d 2163 |
. . 3
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6 | 1, 5 | mtbiri 638 |
. 2
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7 | 6 | necon2ai 2316 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 582 ax-in2 583 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-13 1456 ax-14 1457 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 ax-sep 3978 |
This theorem depends on definitions: df-bi 116 df-tru 1299 df-fal 1302 df-nf 1402 df-sb 1700 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-ne 2263 df-ral 2375 df-v 2635 df-dif 3015 df-nul 3303 df-int 3711 |
This theorem is referenced by: (None) |
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