Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  zfnuleu Unicode version

Theorem zfnuleu 4578
 Description: Show the uniqueness of the empty set (using the Axiom of Extensionality via bm1.1 2440 to strengthen the hypothesis in the form of axnul 4580). (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 1406 . . . . . 6
32albii 1640 . . . . 5
43exbii 1667 . . . 4
51, 4mpbi 208 . . 3
6 nfv 1707 . . . 4
76bm1.1 2440 . . 3
85, 7ax-mp 5 . 2
93eubii 2306 . 2
108, 9mpbir 209 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  <->wb 184  A.wal 1393   wfal 1400  E.wex 1612  E!weu 2282 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-fal 1401  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287
 Copyright terms: Public domain W3C validator