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Theorem difprsn1 4166
Description: Removal of a singleton from an unordered pair. (Contributed by Thierry Arnoux, 4-Feb-2017.)
Assertion
Ref Expression
difprsn1

Proof of Theorem difprsn1
StepHypRef Expression
1 necom 2726 . 2
2 disjsn2 4091 . . . 4
3 disj3 3871 . . . 4
42, 3sylib 196 . . 3
5 df-pr 4032 . . . . . 6
65equncomi 3649 . . . . 5
76difeq1i 3617 . . . 4
8 difun2 3907 . . . 4
97, 8eqtri 2486 . . 3
104, 9syl6reqr 2517 . 2
111, 10sylbir 213 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  =wceq 1395  =/=wne 2652  \cdif 3472  u.cun 3473  i^icin 3474   c0 3784  {csn 4029  {cpr 4031
This theorem is referenced by:  difprsn2  4167  f12dfv  6179  pmtrprfval  16512  usgra1v  24390  cusgra2v  24462  frgra2v  24999  eulerpartlemgf  28318  coinflippvt  28423  ldepsnlinc  33109
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-ne 2654  df-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-sn 4030  df-pr 4032
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