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Mirrors > Home > ILE Home > Th. List > reuhypd | Unicode version |
Description: A theorem useful for eliminating restricted existential uniqueness hypotheses. (Contributed by NM, 16-Jan-2012.) |
Ref | Expression |
---|---|
reuhypd.1 | |
reuhypd.2 |
Ref | Expression |
---|---|
reuhypd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reuhypd.1 | . . . . 5 | |
2 | elex 2610 | . . . . 5 | |
3 | 1, 2 | syl 14 | . . . 4 |
4 | eueq 2763 | . . . 4 | |
5 | 3, 4 | sylib 120 | . . 3 |
6 | eleq1 2141 | . . . . . . 7 | |
7 | 1, 6 | syl5ibrcom 155 | . . . . . 6 |
8 | 7 | pm4.71rd 386 | . . . . 5 |
9 | reuhypd.2 | . . . . . . 7 | |
10 | 9 | 3expa 1138 | . . . . . 6 |
11 | 10 | pm5.32da 439 | . . . . 5 |
12 | 8, 11 | bitr4d 189 | . . . 4 |
13 | 12 | eubidv 1949 | . . 3 |
14 | 5, 13 | mpbid 145 | . 2 |
15 | df-reu 2355 | . 2 | |
16 | 14, 15 | sylibr 132 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 w3a 919 wceq 1284 wcel 1433 weu 1941 wreu 2350 cvv 2601 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-reu 2355 df-v 2603 |
This theorem is referenced by: reuhyp 4222 |
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