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Theorem zfnuleu 4360
 Description: Show the uniqueness of the empty set (using the Axiom of Extensionality via bm1.1 2427 to strengthen the hypothesis in the form of axnul 4362). (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 1335 . . . . . 6
32albii 1576 . . . . 5
43exbii 1593 . . . 4
51, 4mpbi 201 . . 3
6 nfv 1630 . . . 4
76bm1.1 2427 . . 3
85, 7ax-mp 5 . 2
93eubii 2296 . 2
108, 9mpbir 202 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 178   wfal 1327  wal 1550  wex 1551  weu 2287 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-14 1731  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-fal 1330  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2291
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