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Mirrors > Home > MPE Home > Th. List > ssrabeq | Structured version Visualization version 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 3687 | . . 3 | |
2 | 1 | biantru 526 | . 2 |
3 | eqss 3618 | . 2 | |
4 | 2, 3 | bitr4i 267 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wceq 1483 crab 2916 wss 3574 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rab 2921 df-in 3581 df-ss 3588 |
This theorem is referenced by: difrab0eq 4038 |
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