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Theorem zfnuleu 4553
 Description: Show the uniqueness of the empty set (using the Axiom of Extensionality via bm1.1 2412 to strengthen the hypothesis in the form of axnul 4555). (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 1448 . . . . . 6
32albii 1687 . . . . 5
43exbii 1714 . . . 4
51, 4mpbi 211 . . 3
6 nfv 1754 . . . 4
76bm1.1 2412 . . 3
85, 7ax-mp 5 . 2
93eubii 2290 . 2
108, 9mpbir 212 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 187  wal 1435   wfal 1442  wex 1659  weu 2266 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-9 1874  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-fal 1443  df-ex 1660  df-nf 1664  df-sb 1790  df-eu 2270  df-mo 2271 This theorem is referenced by: (None)
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