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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 | |
3eqtr3a.2 | |
3eqtr3a.3 |
Ref | Expression |
---|---|
3eqtr3a |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3eqtr3a.2 | . 2 | |
2 | 3eqtr3a.1 | . . 3 | |
3 | 3eqtr3a.3 | . . 3 | |
4 | 2, 3 | syl5eq 2125 | . 2 |
5 | 1, 4 | eqtr3d 2115 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1284 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-4 1440 ax-17 1459 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-cleq 2074 |
This theorem is referenced by: uneqin 3215 coi2 4857 foima 5131 f1imacnv 5163 fvsnun2 5382 phplem4 6341 phplem4on 6353 halfnqq 6600 resqrexlemcalc1 9900 |
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