Description: There exists at most one set with prescribed elements. Theorem 1.1 of BellMachover p. 462. (Contributed by NM, 30-Jun-1994) (Proof shortened by Wolf Lammen, 13-Nov-2019) Use the at-most-one quantifier. (Revised by BJ, 17-Sep-2022)
Ref | Expression | ||
---|---|---|---|
Hypothesis | axextmo.1 | |
|
Assertion | axextmo | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axextmo.1 | |
|
2 | biantr | |
|
3 | 2 | alanimi | |
4 | ax-ext | |
|
5 | 3 4 | syl | |
6 | 5 | gen2 | |
7 | nfv | |
|
8 | 7 1 | nfbi | |
9 | 8 | nfal | |
10 | elequ2 | |
|
11 | 10 | bibi1d | |
12 | 11 | albidv | |
13 | 9 12 | mo4f | |
14 | 6 13 | mpbir | |