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Mirrors > Home > ILE Home > Th. List > 3eqtr3a | Unicode version |
Description: A chained equality inference, useful for converting from definitions. (Contributed by Mario Carneiro, 6-Nov-2015.) |
Ref | Expression |
---|---|
3eqtr3a.1 |
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3eqtr3a.2 |
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3eqtr3a.3 |
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Ref | Expression |
---|---|
3eqtr3a |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3eqtr3a.2 |
. 2
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2 | 3eqtr3a.1 |
. . 3
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3 | 3eqtr3a.3 |
. . 3
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4 | 2, 3 | syl5eq 2139 |
. 2
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5 | 1, 4 | eqtr3d 2129 |
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 105 ax-ia2 106 ax-ia3 107 ax-5 1388 ax-gen 1390 ax-4 1452 ax-17 1471 ax-ext 2077 |
This theorem depends on definitions: df-bi 116 df-cleq 2088 |
This theorem is referenced by: uneqin 3266 coi2 4981 foima 5273 f1imacnv 5305 fvsnun2 5534 fnsnsplitdc 6304 phplem4 6651 phplem4on 6663 halfnqq 7066 resqrexlemcalc1 10578 absefib 11224 efieq1re 11225 restopnb 12048 |
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