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Mirrors > Home > ILE Home > Th. List > eqrd | Unicode version |
Description: Deduce equality of classes from equivalence of membership. (Contributed by Thierry Arnoux, 21-Mar-2017.) |
Ref | Expression |
---|---|
eqrd.0 |
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eqrd.1 |
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eqrd.2 |
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eqrd.3 |
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Ref | Expression |
---|---|
eqrd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqrd.0 |
. . 3
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2 | eqrd.1 |
. . 3
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3 | eqrd.2 |
. . 3
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4 | eqrd.3 |
. . . 4
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5 | 4 | biimpd 132 |
. . 3
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6 | 1, 2, 3, 5 | ssrd 2944 |
. 2
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7 | 4 | biimprd 147 |
. . 3
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8 | 1, 3, 2, 7 | ssrd 2944 |
. 2
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9 | 6, 8 | eqssd 2956 |
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-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-in 2918 df-ss 2925 |
This theorem is referenced by: (None) |
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