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Theorem bm1.1 2456
 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.)
Hypothesis
Ref Expression
bm1.1.1
Assertion
Ref Expression
bm1.1
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem bm1.1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 biantr 945 . . . . 5
21alanimi 1696 . . . 4
3 ax-ext 2451 . . . 4
42, 3syl 17 . . 3
54gen2 1678 . 2
6 nfv 1769 . . . . . 6
7 bm1.1.1 . . . . . 6
86, 7nfbi 2037 . . . . 5
98nfal 2049 . . . 4
10 elequ2 1918 . . . . . 6
1110bibi1d 326 . . . . 5
1211albidv 1775 . . . 4
139, 12mo4f 2365 . . 3
14 df-mo 2324 . . 3
1513, 14bitr3i 259 . 2
165, 15mpbi 213 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376  wal 1450  wex 1671  wnf 1675  weu 2319  wmo 2320 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324 This theorem is referenced by:  zfnuleu  4523
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