Theorem sucel 4956

Description: Membership of a successor in another class. (Contributed by NM, 29-Jun-2004.)

Assertion

Ref	Expression
sucel

Distinct variable groups:   ,,   ,

Proof of Theorem sucel

Step	Hyp	Ref	Expression
1		risset 2982	. 2
2		dfcleq 2450	. . . 4
3		vex 3112	. . . . . . 7
4	3	elsuc 4952	. . . . . 6
5	4	bibi2i 313	. . . . 5
6	5	albii 1640	. . . 4
7	2, 6	bitri 249	. . 3
8	7	rexbii 2959	. 2
9	1, 8	bitri 249	1

Syntax hints:  <->wb 184  \/wo 368  A.wal 1393  =wceq 1395  e.wcel 1818  E.wrex 2808  succsuc 4885

This theorem is referenced by:  axinf2  8078  zfinf2  8080

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-rex 2813  df-v 3111  df-un 3480  df-sn 4030  df-suc 4889