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Mirrors > Home > MPE Home > Th. List > snriota | Structured version Visualization version Unicode version |
Description: A restricted class abstraction with a unique member can be expressed as a singleton. (Contributed by NM, 30-May-2006.) |
Ref | Expression |
---|---|
snriota |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-reu 2919 | . . 3 | |
2 | sniota 5878 | . . 3 | |
3 | 1, 2 | sylbi 207 | . 2 |
4 | df-rab 2921 | . 2 | |
5 | df-riota 6611 | . . 3 | |
6 | 5 | sneqi 4188 | . 2 |
7 | 3, 4, 6 | 3eqtr4g 2681 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 weu 2470 cab 2608 wreu 2914 crab 2916 csn 4177 cio 5849 crio 6610 |
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-eu 2474 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 df-un 3579 df-sn 4178 df-pr 4180 df-uni 4437 df-iota 5851 df-riota 6611 |
This theorem is referenced by: divalgmod 15129 divalgmodOLD 15130 |
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