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Theorem bm1.1 2440
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:   ,

Proof of Theorem bm1.1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 biantr 931 . . . . 5
21alanimi 1637 . . . 4
3 ax-ext 2435 . . . 4
42, 3syl 16 . . 3
54gen2 1619 . 2
6 nfv 1707 . . . . . 6
7 bm1.1.1 . . . . . 6
86, 7nfbi 1934 . . . . 5
98nfal 1947 . . . 4
10 elequ2 1823 . . . . . 6
1110bibi1d 319 . . . . 5
1211albidv 1713 . . . 4
139, 12mo4f 2336 . . 3
14 df-mo 2287 . . 3
1513, 14bitr3i 251 . 2
165, 15mpbi 208 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612  F/wnf 1616  E!weu 2282  E*wmo 2283
This theorem is referenced by:  zfnuleu  4578
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287
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