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Theorem bm1.1 2238
 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.)
Hypothesis
Ref Expression
bm1.1.1
Assertion
Ref Expression
bm1.1
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem bm1.1
StepHypRef Expression
1 nfv 1629 . . . . . . . 8
2 bm1.1.1 . . . . . . . 8
31, 2nfbi 1738 . . . . . . 7
43nfal 1732 . . . . . 6
5 elequ2 1832 . . . . . . . 8
65bibi1d 312 . . . . . . 7
76albidv 2004 . . . . . 6
84, 7sbie 1910 . . . . 5
9 19.26 1592 . . . . . 6
10 biantr 902 . . . . . . . 8
1110alimi 1546 . . . . . . 7
12 ax-ext 2234 . . . . . . 7
1311, 12syl 17 . . . . . 6
149, 13sylbir 206 . . . . 5
158, 14sylan2b 463 . . . 4
1615gen2 1541 . . 3
1716jctr 528 . 2
18 nfv 1629 . . 3
1918eu2 2138 . 2
2017, 19sylibr 205 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360  wal 1532  wex 1537  wnf 1539   wceq 1619   wcel 1621  wsb 1882  weu 2114 This theorem is referenced by:  zfnuleu  4043 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-eu 2118
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