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Theorem zfnuleu 4043
 Description: Show the uniqueness of the empty set (using the Axiom of Extensionality via bm1.1 2238 to strengthen the hypothesis in the form of axnul 4045). (Contributed by NM, 22-Dec-2007.)
Hypothesis
Ref Expression
zfnuleu.1
Assertion
Ref Expression
zfnuleu
Distinct variable group:   ,

Proof of Theorem zfnuleu
StepHypRef Expression
1 zfnuleu.1 . . . 4
2 nbfal 1322 . . . . . 6
32albii 1554 . . . . 5
43exbii 1580 . . . 4
51, 4mpbi 201 . . 3
6 nfv 1629 . . . 4
76bm1.1 2238 . . 3
85, 7ax-mp 10 . 2
93eubii 2123 . 2
108, 9mpbir 202 1
 Colors of variables: wff set class Syntax hints:   wn 5   wb 178   wfal 1313  wal 1532  wex 1537   wcel 1621  weu 2114 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-fal 1316  df-ex 1538  df-nf 1540  df-sb 1883  df-eu 2118
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