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Theorem intunsn 3965
 Description: Theorem joining a singleton to an intersection. (Contributed by NM, 29-Sep-2002.)
Hypothesis
Ref Expression
intunsn.1 B V
Assertion
Ref Expression
intunsn (A ∪ {B}) = (AB)

Proof of Theorem intunsn
StepHypRef Expression
1 intun 3958 . 2 (A ∪ {B}) = (A{B})
2 intunsn.1 . . . 4 B V
32intsn 3962 . . 3 {B} = B
43ineq2i 3454 . 2 (A{B}) = (AB)
51, 4eqtri 2373 1 (A ∪ {B}) = (AB)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642   ∈ wcel 1710  Vcvv 2859   ∪ cun 3207   ∩ cin 3208  {csn 3737  ∩cint 3926 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-sn 3741  df-pr 3742  df-int 3927 This theorem is referenced by: (None)
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