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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 3971 |
. . 3
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2 | inteq 3691 |
. . . . 5
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3 | int0 3702 |
. . . . 5
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4 | 2, 3 | syl6eq 2136 |
. . . 4
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5 | 4 | eleq1d 2156 |
. . 3
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6 | 1, 5 | mtbiri 635 |
. 2
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7 | 6 | necon2ai 2309 |
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 104 ax-ia2 105 ax-ia3 106 ax-in1 579 ax-in2 580 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-13 1449 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3957 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-fal 1295 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ne 2256 df-ral 2364 df-v 2621 df-dif 3001 df-nul 3287 df-int 3689 |
This theorem is referenced by: (None) |
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