Theorem elsnc2g 4059

Description: There is only one element in a singleton. Exercise 2 of [TakeutiZaring] p. 15. This variation requires only that , rather than , be a set. (Contributed by NM, 28-Oct-2003.)

Assertion

Ref	Expression
elsnc2g

Proof of Theorem elsnc2g

Step	Hyp	Ref	Expression
1		elsni 4054	. 2
2		snidg 4055	. . 3
3		eleq1 2529	. . 3
4	2, 3	syl5ibrcom 222	. 2
5	1, 4	impbid2 204	1

Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  e.wcel 1818  {csn 4029

This theorem is referenced by:  elsnc2  4060  elsuc2g  4951  mptiniseg  5506  extmptsuppeq  6943  fzosplitsni  11920  limcco  22297  ply1termlem  22600  stirlinglem8  31863  dirkercncflem2  31886  elpmapat  35488

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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-sn 4030