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Mirrors > Home > ILE Home > Th. List > intnexr | Unicode version |
Description: If a class intersection is the universe, it is not a set. In classical logic this would be an equivalence. (Contributed by Jim Kingdon, 27-Aug-2018.) |
Ref | Expression |
---|---|
intnexr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vprc 4150 |
. 2
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2 | eleq1 2252 |
. 2
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3 | 1, 2 | mtbiri 676 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-v 2754 |
This theorem is referenced by: (None) |
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