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Theorem bm1.1 2142
 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 1508 . . . . . . . 8
2 bm1.1.1 . . . . . . . 8
31, 2nfbi 1569 . . . . . . 7
43nfal 1556 . . . . . 6
5 elequ2 2133 . . . . . . . 8
65bibi1d 232 . . . . . . 7
76albidv 1804 . . . . . 6
84, 7sbie 1771 . . . . 5
9 19.26 1461 . . . . . 6
10 biantr 937 . . . . . . . 8
1110alimi 1435 . . . . . . 7
12 ax-ext 2139 . . . . . . 7
1311, 12syl 14 . . . . . 6
149, 13sylbir 134 . . . . 5
158, 14sylan2b 285 . . . 4
1615gen2 1430 . . 3
1716jctr 313 . 2
18 nfv 1508 . . 3
1918eu2 2050 . 2
2017, 19sylibr 133 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1333  wnf 1440  wex 1472  wsb 1742  weu 2006 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-14 2131  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-eu 2009 This theorem is referenced by:  zfnuleu  4088
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