Theorem elsuc2 2293

Description: Membership in a successor.

Hypothesis

Ref	Expression
elsuc.1	|- A e. V

Assertion

Ref	Expression
elsuc2	|- (B e. suc A <-> (B e. A \/ B = A))

Proof of Theorem elsuc2

Step	Hyp	Ref	Expression
1		elsuc.1	. 2 |- A e. V
2		elsuc2g 2291	. 2 |- (A e. V -> (B e. suc A <-> (B e. A \/ B = A)))
3	1, 2	ax-mp 6	1 |- (B e. suc A <-> (B e. A \/ B = A))

Syntax hints:   <-> wb 127   \/ wo 195   = wceq 1091   e. wcel 1092  Vcvv 1348  suc csuc 2201

This theorem is referenced by:  alephordi 3679

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-un 1490  df-sn 1811  df-pr 1812  df-suc 2205

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