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Theorem difprsnss 3963
 Description: Removal of a singleton from an unordered pair. (Contributed by NM, 16-Mar-2006.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
difprsnss

Proof of Theorem difprsnss
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2968 . . . . 5
21elpr 3861 . . . 4
3 elsn 3858 . . . . 5
43notbii 289 . . . 4
5 biorf 396 . . . . 5
65biimparc 475 . . . 4
72, 4, 6syl2anb 467 . . 3
8 eldif 3319 . . 3
9 elsn 3858 . . 3
107, 8, 93imtr4i 259 . 2
1110ssriv 3341 1
 Colors of variables: wff set class Syntax hints:   wn 3   wo 359   wa 360   wceq 1654   wcel 1728   cdif 3306   wss 3309  csn 3843  cpr 3844 This theorem is referenced by:  itg11  19619  en2other2  27471  pmtrprfv  27485 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-v 2967  df-dif 3312  df-un 3314  df-in 3316  df-ss 3323  df-sn 3849  df-pr 3850
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