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

Step	Hyp	Ref	Expression
1		zfnuleu.1	. . . 4
2		nbfal 1406	. . . . . 6
3	2	albii 1640	. . . . 5
4	3	exbii 1667	. . . 4
5	1, 4	mpbi 208	. . 3
6		nfv 1707	. . . 4
7	6	bm1.1 2440	. . 3
8	5, 7	ax-mp 5	. 2
9	3	eubii 2306	. 2
10	8, 9	mpbir 209	1

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