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Mirrors > Home > MPE Home > Th. List > euf | Structured version Visualization version Unicode version |
Description: A version of the existential uniqueness definition with a hypothesis instead of a distinct variable condition. (Contributed by NM, 12-Aug-1993.) (Proof shortened by Wolf Lammen, 30-Oct-2018.) |
Ref | Expression |
---|---|
euf.1 |
Ref | Expression |
---|---|
euf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eu 2474 | . 2 | |
2 | euf.1 | . . . . 5 | |
3 | nfv 1843 | . . . . 5 | |
4 | 2, 3 | nfbi 1833 | . . . 4 |
5 | 4 | nfal 2153 | . . 3 |
6 | nfv 1843 | . . 3 | |
7 | equequ2 1953 | . . . . 5 | |
8 | 7 | bibi2d 332 | . . . 4 |
9 | 8 | albidv 1849 | . . 3 |
10 | 5, 6, 9 | cbvex 2272 | . 2 |
11 | 1, 10 | bitri 264 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wal 1481 wex 1704 wnf 1708 weu 2470 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-eu 2474 |
This theorem is referenced by: eu1 2510 bj-eumo0 32830 |
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