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Mirrors > Home > MPE Home > Th. List > reu6i | Structured version Visualization version Unicode version |
Description: A condition which implies existential uniqueness. (Contributed by Mario Carneiro, 2-Oct-2015.) |
Ref | Expression |
---|---|
reu6i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq2 2633 | . . . . 5 | |
2 | 1 | bibi2d 332 | . . . 4 |
3 | 2 | ralbidv 2986 | . . 3 |
4 | 3 | rspcev 3309 | . 2 |
5 | reu6 3395 | . 2 | |
6 | 4, 5 | sylibr 224 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wcel 1990 wral 2912 wrex 2913 wreu 2914 |
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-v 3202 |
This theorem is referenced by: eqreu 3398 riota5f 6636 negeu 10271 creur 11014 creui 11015 reuccats1 13480 lublecl 16989 dfod2 17981 lmieu 25676 esum2dlem 30154 poimirlem16 33425 poimirlem17 33426 poimirlem19 33428 poimirlem20 33429 poimirlem22 33431 reuccatpfxs1 41434 |
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