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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 2555 |
. . . 4
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2 | eueq 2706 |
. . . 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 1901 |
. 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 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-sb 1643 df-eu 1900 df-mo 1901 df-clab 2024 df-cleq 2030 df-clel 2033 df-v 2553 |
This theorem is referenced by: euxfr2dc 2720 reueq 2732 mosn 3398 sndisj 3751 disjxsn 3753 reusv1 4156 funopabeq 4879 funcnvsn 4888 fvmptg 5191 fvopab6 5207 ovmpt4g 5565 ovi3 5579 ov6g 5580 oprabex3 5698 1stconst 5784 2ndconst 5785 |
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