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Mirrors > Home > ILE Home > Th. List > ssrabeq | Unicode version |
Description: If the restricting class of a restricted class abstraction is a subset of this restricted class abstraction, it is equal to this restricted class abstraction. (Contributed by Alexander van der Vekens, 31-Dec-2017.) |
Ref | Expression |
---|---|
ssrabeq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssrab2 3079 | . . 3 | |
2 | 1 | biantru 296 | . 2 |
3 | eqss 3014 | . 2 | |
4 | 2, 3 | bitr4i 185 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 102 wb 103 wceq 1284 crab 2352 wss 2973 |
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-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rab 2357 df-in 2979 df-ss 2986 |
This theorem is referenced by: difrab0eqim 3310 |
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