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Mirrors > Home > ILE Home > Th. List > euxfrdc | Unicode version |
Description: Transfer existential uniqueness from a variable to another variable contained in expression . (Contributed by NM, 14-Nov-2004.) |
Ref | Expression |
---|---|
euxfrdc.1 | |
euxfrdc.2 | |
euxfrdc.3 |
Ref | Expression |
---|---|
euxfrdc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euxfrdc.2 | . . . . . 6 | |
2 | euex 2029 | . . . . . 6 | |
3 | 1, 2 | ax-mp 5 | . . . . 5 |
4 | 3 | biantrur 301 | . . . 4 |
5 | 19.41v 1874 | . . . 4 | |
6 | euxfrdc.3 | . . . . . 6 | |
7 | 6 | pm5.32i 449 | . . . . 5 |
8 | 7 | exbii 1584 | . . . 4 |
9 | 4, 5, 8 | 3bitr2i 207 | . . 3 |
10 | 9 | eubii 2008 | . 2 |
11 | euxfrdc.1 | . . 3 | |
12 | 1 | eumoi 2032 | . . 3 |
13 | 11, 12 | euxfr2dc 2869 | . 2 DECID |
14 | 10, 13 | syl5bb 191 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 DECID wdc 819 wceq 1331 wex 1468 wcel 1480 weu 1999 cvv 2686 |
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-in1 603 ax-in2 604 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-dc 820 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-v 2688 |
This theorem is referenced by: (None) |
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