Theorem intsn 4323

Description: The intersection of a singleton is its member. Theorem 70 of [Suppes] p. 41. (Contributed by NM, 29-Sep-2002.)

Hypothesis

Ref	Expression
intsn.1

Assertion

Ref	Expression
intsn

Proof of Theorem intsn

Step	Hyp	Ref	Expression
1		intsn.1	. 2
2		intsng 4322	. 2
3	1, 2	ax-mp 5	1

Syntax hints:  =wceq 1395  e.wcel 1818  cvv 3109  {csn 4029  |^|cint 4286

This theorem is referenced by:  uniintsn  4324  intunsn  4326  op1stb  4722  op2ndb  5497  ssfii  7899  cf0  8652  cflecard  8654  uffix  20422  iotain  31324

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-3an 975  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-ral 2812  df-v 3111  df-un 3480  df-in 3482  df-sn 4030  df-pr 4032  df-int 4287