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Mirrors > Home > ILE Home > Th. List > moeq | Unicode version |
Description: There is at most one set equal to a class. (Contributed by NM, 8-Mar-1995.) |
Ref | Expression |
---|---|
moeq |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isset 2561 |
. . . 4
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2 | eueq 2712 |
. . . 4
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3 | 1, 2 | bitr3i 175 |
. . 3
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4 | 3 | biimpi 113 |
. 2
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5 | df-mo 1904 |
. 2
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6 | 4, 5 | mpbir 134 |
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 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-v 2559 |
This theorem is referenced by: euxfr2dc 2726 reueq 2738 mosn 3406 sndisj 3760 disjxsn 3762 reusv1 4190 funopabeq 4936 funcnvsn 4945 fvmptg 5248 fvopab6 5264 ovmpt4g 5623 ovi3 5637 ov6g 5638 oprabex3 5756 1stconst 5842 2ndconst 5843 |
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