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Mirrors > Home > ILE Home > Th. List > eqeq12 | Unicode version |
Description: Equality relationship among 4 classes. (Contributed by NM, 3-Aug-1994.) |
Ref | Expression |
---|---|
eqeq12 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 2147 |
. 2
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2 | eqeq2 2150 |
. 2
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3 | 1, 2 | sylan9bb 458 |
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 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-gen 1426 ax-4 1488 ax-17 1507 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-cleq 2133 |
This theorem is referenced by: eqeq12i 2154 eqeq12d 2155 eqeqan12d 2156 funopg 5165 tfri3 6272 th3qlem1 6539 xpdom2 6733 difinfsnlem 6992 difinfsn 6993 xrlttri3 9613 bcn1 10536 summodc 11184 prodmodc 11379 |
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