Theorem intunsn 4326

Description: Theorem joining a singleton to an intersection. (Contributed by NM, 29-Sep-2002.)

Hypothesis

Ref	Expression
intunsn.1

Assertion

Ref	Expression
intunsn

Proof of Theorem intunsn

Step	Hyp	Ref	Expression
1		intun 4319	. 2
2		intunsn.1	. . . 4
3	2	intsn 4323	. . 3
4	3	ineq2i 3696	. 2
5	1, 4	eqtri 2486	1

Syntax hints:  =wceq 1395  e.wcel 1818  cvv 3109  u.cun 3473  i^icin 3474  {csn 4029  |^|cint 4286

This theorem is referenced by:  fiint  7817  incexclem  13648  heibor1lem  30305

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