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Mirrors > Home > ILE Home > Th. List > euexex | Unicode version |
Description: Existential uniqueness and "at most one" double quantification. (Contributed by Jim Kingdon, 28-Dec-2018.) |
Ref | Expression |
---|---|
euexex.1 |
Ref | Expression |
---|---|
euexex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eu5 2046 | . . 3 | |
2 | nfmo1 2011 | . . . . . 6 | |
3 | nfa1 1521 | . . . . . . 7 | |
4 | nfe1 1472 | . . . . . . . 8 | |
5 | 4 | nfmo 2019 | . . . . . . 7 |
6 | 3, 5 | nfim 1551 | . . . . . 6 |
7 | 2, 6 | nfim 1551 | . . . . 5 |
8 | euexex.1 | . . . . . . 7 | |
9 | 8 | nfmo 2019 | . . . . . . 7 |
10 | mopick 2077 | . . . . . . . . 9 | |
11 | 10 | ex 114 | . . . . . . . 8 |
12 | 11 | com3r 79 | . . . . . . 7 |
13 | 8, 9, 12 | alrimd 1589 | . . . . . 6 |
14 | moim 2063 | . . . . . . 7 | |
15 | 14 | spsd 1518 | . . . . . 6 |
16 | 13, 15 | syl6 33 | . . . . 5 |
17 | 7, 16 | exlimi 1573 | . . . 4 |
18 | 17 | imp 123 | . . 3 |
19 | 1, 18 | sylbi 120 | . 2 |
20 | 19 | imp 123 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1329 wnf 1436 wex 1468 weu 1999 wmo 2000 |
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 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 |
This theorem is referenced by: mosubt 2861 funco 5163 |
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