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Mirrors > Home > ILE Home > Th. List > eueq | Unicode version |
Description: Equality has existential uniqueness. (Contributed by NM, 25-Nov-1994.) |
Ref | Expression |
---|---|
eueq |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqtr3 2207 |
. . . 4
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2 | 1 | gen2 1460 |
. . 3
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3 | 2 | biantru 302 |
. 2
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4 | isset 2755 |
. 2
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5 | eqeq1 2194 |
. . 3
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6 | 5 | eu4 2098 |
. 2
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7 | 3, 4, 6 | 3bitr4i 212 |
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 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-nf 1471 df-sb 1773 df-eu 2039 df-mo 2040 df-clab 2174 df-cleq 2180 df-clel 2183 df-v 2751 |
This theorem is referenced by: eueq1 2921 moeq 2924 mosubt 2926 reuhypd 4483 mptfng 5353 upxp 14068 |
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