New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > eu2 | Unicode version |
Description: An alternate way of defining existential uniqueness. Definition 6.10 of [TakeutiZaring] p. 26. (Contributed by NM, 8-Jul-1994.) |
Ref | Expression |
---|---|
eu2.1 |
Ref | Expression |
---|---|
eu2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euex 2227 | . . 3 | |
2 | eu2.1 | . . . . 5 | |
3 | 2 | eumo0 2228 | . . . 4 |
4 | 2 | mo 2226 | . . . 4 |
5 | 3, 4 | sylib 188 | . . 3 |
6 | 1, 5 | jca 518 | . 2 |
7 | 19.29r 1597 | . . . 4 | |
8 | impexp 433 | . . . . . . . . 9 | |
9 | 8 | albii 1566 | . . . . . . . 8 |
10 | 2 | 19.21 1796 | . . . . . . . 8 |
11 | 9, 10 | bitri 240 | . . . . . . 7 |
12 | 11 | anbi2i 675 | . . . . . 6 |
13 | abai 770 | . . . . . 6 | |
14 | 12, 13 | bitr4i 243 | . . . . 5 |
15 | 14 | exbii 1582 | . . . 4 |
16 | 7, 15 | sylib 188 | . . 3 |
17 | 2 | eu1 2225 | . . 3 |
18 | 16, 17 | sylibr 203 | . 2 |
19 | 6, 18 | impbii 180 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wal 1540 wex 1541 wnf 1544 wsb 1648 weu 2204 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 |
This theorem is referenced by: eu3 2230 bm1.1 2338 reu2 3024 |
Copyright terms: Public domain | W3C validator |