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Mirrors > Home > MPE Home > Th. List > bm1.1 | Structured version Visualization version Unicode version |
Description: Any set defined by a property is the only set defined by that property. Theorem 1.1 of [BellMachover] p. 462. (Contributed by NM, 30-Jun-1994.) (Proof shortened by Wolf Lammen, 13-Nov-2019.) |
Ref | Expression |
---|---|
bm1.1.1 |
Ref | Expression |
---|---|
bm1.1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | biantr 972 | . . . . 5 | |
2 | 1 | alanimi 1744 | . . . 4 |
3 | ax-ext 2602 | . . . 4 | |
4 | 2, 3 | syl 17 | . . 3 |
5 | 4 | gen2 1723 | . 2 |
6 | nfv 1843 | . . . . . 6 | |
7 | bm1.1.1 | . . . . . 6 | |
8 | 6, 7 | nfbi 1833 | . . . . 5 |
9 | 8 | nfal 2153 | . . . 4 |
10 | elequ2 2004 | . . . . . 6 | |
11 | 10 | bibi1d 333 | . . . . 5 |
12 | 11 | albidv 1849 | . . . 4 |
13 | 9, 12 | mo4f 2516 | . . 3 |
14 | df-mo 2475 | . . 3 | |
15 | 13, 14 | bitr3i 266 | . 2 |
16 | 5, 15 | mpbi 220 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wal 1481 wex 1704 wnf 1708 weu 2470 wmo 2471 |
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-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 |
This theorem is referenced by: zfnuleu 4786 |
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