Theorem elsuc 4952

Description: Membership in a successor. Exercise 5 of [TakeutiZaring] p. 17. (Contributed by NM, 15-Sep-2003.)

Hypothesis

Ref	Expression
elsuc.1

Assertion

Ref	Expression
elsuc

Proof of Theorem elsuc

Step	Hyp	Ref	Expression
1		elsuc.1	. 2
2		elsucg 4950	. 2
3	1, 2	ax-mp 5	1

Syntax hints:  <->wb 184  \/wo 368  =wceq 1395  e.wcel 1818  cvv 3109  succsuc 4885

This theorem is referenced by:  sucel  4956  suctr  4966  limsssuc  6685  omsmolem  7321  cantnfle  8111  cantnfleOLD  8141  infxpenlem  8412  inatsk  9177  untsucf  29082  dfon2lem7  29221

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-or 370  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-un 3480  df-sn 4030  df-suc 4889