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Mirrors > Home > ILE Home > Th. List > euxfr2dc | Unicode version |
Description: Transfer existential uniqueness from a variable to another variable contained in expression . (Contributed by NM, 14-Nov-2004.) |
Ref | Expression |
---|---|
euxfr2dc.1 | |
euxfr2dc.2 |
Ref | Expression |
---|---|
euxfr2dc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euxfr2dc.2 | . . . . . . 7 | |
2 | 1 | moani 2083 | . . . . . 6 |
3 | ancom 264 | . . . . . . 7 | |
4 | 3 | mobii 2050 | . . . . . 6 |
5 | 2, 4 | mpbi 144 | . . . . 5 |
6 | 5 | ax-gen 1436 | . . . 4 |
7 | excom 1651 | . . . . . 6 | |
8 | 7 | dcbii 830 | . . . . 5 DECID DECID |
9 | 2euswapdc 2104 | . . . . 5 DECID | |
10 | 8, 9 | sylbi 120 | . . . 4 DECID |
11 | 6, 10 | mpi 15 | . . 3 DECID |
12 | moeq 2896 | . . . . . . 7 | |
13 | 12 | moani 2083 | . . . . . 6 |
14 | 3 | mobii 2050 | . . . . . 6 |
15 | 13, 14 | mpbi 144 | . . . . 5 |
16 | 15 | ax-gen 1436 | . . . 4 |
17 | 2euswapdc 2104 | . . . 4 DECID | |
18 | 16, 17 | mpi 15 | . . 3 DECID |
19 | 11, 18 | impbid 128 | . 2 DECID |
20 | euxfr2dc.1 | . . . 4 | |
21 | biidd 171 | . . . 4 | |
22 | 20, 21 | ceqsexv 2760 | . . 3 |
23 | 22 | eubii 2022 | . 2 |
24 | 19, 23 | bitrdi 195 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 DECID wdc 824 wal 1340 wceq 1342 wex 1479 weu 2013 wmo 2014 wcel 2135 cvv 2721 |
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 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-dc 825 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-v 2723 |
This theorem is referenced by: euxfrdc 2907 |
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