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Theorem bm1.1 2268
 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
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1605 . . . . . . . 8
2 bm1.1.1 . . . . . . . 8
31, 2nfbi 1772 . . . . . . 7
43nfal 1766 . . . . . 6
5 elequ2 1689 . . . . . . . 8
65bibi1d 310 . . . . . . 7
76albidv 1611 . . . . . 6
84, 7sbie 1978 . . . . 5
9 19.26 1580 . . . . . 6
10 biantr 897 . . . . . . . 8
1110alimi 1546 . . . . . . 7
12 ax-ext 2264 . . . . . . 7
1311, 12syl 15 . . . . . 6
149, 13sylbir 204 . . . . 5
158, 14sylan2b 461 . . . 4
1615gen2 1534 . . 3
1716jctr 526 . 2
18 nfv 1605 . . 3
1918eu2 2168 . 2
2017, 19sylibr 203 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wal 1527  wex 1528  wnf 1531   wceq 1623  wsb 1629   wcel 1684  weu 2143 This theorem is referenced by:  zfnuleu  4146 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147
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