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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 3182 | . . 3 | |
2 | 1 | biantru 300 | . 2 |
3 | eqss 3112 | . 2 | |
4 | 2, 3 | bitr4i 186 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1331 crab 2420 wss 3071 |
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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rab 2425 df-in 3077 df-ss 3084 |
This theorem is referenced by: difrab0eqim 3429 |
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