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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 2047 | . . . . . 6 |
3 | ancom 264 | . . . . . . 7 | |
4 | 3 | mobii 2014 | . . . . . 6 |
5 | 2, 4 | mpbi 144 | . . . . 5 |
6 | 5 | ax-gen 1410 | . . . 4 |
7 | excom 1627 | . . . . . 6 | |
8 | 7 | dcbii 810 | . . . . 5 DECID DECID |
9 | 2euswapdc 2068 | . . . . 5 DECID | |
10 | 8, 9 | sylbi 120 | . . . 4 DECID |
11 | 6, 10 | mpi 15 | . . 3 DECID |
12 | moeq 2832 | . . . . . . 7 | |
13 | 12 | moani 2047 | . . . . . 6 |
14 | 3 | mobii 2014 | . . . . . 6 |
15 | 13, 14 | mpbi 144 | . . . . 5 |
16 | 15 | ax-gen 1410 | . . . 4 |
17 | 2euswapdc 2068 | . . . 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 2699 | . . 3 |
23 | 22 | eubii 1986 | . 2 |
24 | 19, 23 | syl6bb 195 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 DECID wdc 804 wal 1314 wceq 1316 wex 1453 wcel 1465 weu 1977 wmo 1978 cvv 2660 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-dc 805 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-v 2662 |
This theorem is referenced by: euxfrdc 2843 |
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