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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 2741 | . . . . 5 | |
3 | 1, 2 | syl 14 | . . . 4 |
4 | eueq 2901 | . . . 4 | |
5 | 3, 4 | sylib 121 | . . 3 |
6 | eleq1 2233 | . . . . . . 7 | |
7 | 1, 6 | syl5ibrcom 156 | . . . . . 6 |
8 | 7 | pm4.71rd 392 | . . . . 5 |
9 | reuhypd.2 | . . . . . . 7 | |
10 | 9 | 3expa 1198 | . . . . . 6 |
11 | 10 | pm5.32da 449 | . . . . 5 |
12 | 8, 11 | bitr4d 190 | . . . 4 |
13 | 12 | eubidv 2027 | . . 3 |
14 | 5, 13 | mpbid 146 | . 2 |
15 | df-reu 2455 | . 2 | |
16 | 14, 15 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 973 wceq 1348 weu 2019 wcel 2141 wreu 2450 cvv 2730 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-reu 2455 df-v 2732 |
This theorem is referenced by: reuhyp 4457 |
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