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Theorem difprsnss 3846
 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 2862 . . . . 5
21elpr 3751 . . . 4
3 elsn 3748 . . . . 5
43notbii 287 . . . 4
5 biorf 394 . . . . 5
65biimparc 473 . . . 4
72, 4, 6syl2anb 465 . . 3
8 eldif 3221 . . 3
9 elsn 3748 . . 3
107, 8, 93imtr4i 257 . 2
1110ssriv 3277 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wo 357   wa 358   wceq 1642   wcel 1710   cdif 3206   wss 3257  csn 3737  cpr 3738 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-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-sn 3741  df-pr 3742 This theorem is referenced by: (None)
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