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Theorem bm1.1 2393
 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 1626 . . . . . . . 8
2 bm1.1.1 . . . . . . . 8
31, 2nfbi 1852 . . . . . . 7
43nfal 1860 . . . . . 6
5 elequ2 1726 . . . . . . . 8
65bibi1d 311 . . . . . . 7
76albidv 1632 . . . . . 6
84, 7sbie 2091 . . . . 5
9 19.26 1600 . . . . . 6
10 biantr 898 . . . . . . . 8
1110alimi 1565 . . . . . . 7
12 ax-ext 2389 . . . . . . 7
1311, 12syl 16 . . . . . 6
149, 13sylbir 205 . . . . 5
158, 14sylan2b 462 . . . 4
1615gen2 1553 . . 3
1716jctr 527 . 2
18 nfv 1626 . . 3
1918eu2 2283 . 2
2017, 19sylibr 204 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1546  wex 1547  wnf 1550  wsb 1655  weu 2258 This theorem is referenced by:  zfnuleu  4299 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2262
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