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Mirrors > Home > ILE Home > Th. List > mopnrel | Unicode version |
Description: The class of open sets of a metric space is a relation. (Contributed by Jim Kingdon, 5-May-2023.) |
Ref | Expression |
---|---|
mopnrel |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mptrel 4755 |
. 2
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2 | df-mopn 13387 |
. . 3
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3 | 2 | releqi 4709 |
. 2
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4 | 1, 3 | mpbir 146 |
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-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4121 ax-pow 4174 ax-pr 4209 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-opab 4065 df-mpt 4066 df-xp 4632 df-rel 4633 df-mopn 13387 |
This theorem is referenced by: isxms2 13888 |
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