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Theorem difprsn 3756
 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
difprsn

Proof of Theorem difprsn
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2791 . . . . 5
21elpr 3658 . . . 4
3 elsn 3655 . . . . 5
43notbii 287 . . . 4
5 biorf 394 . . . . 5
65biimparc 473 . . . 4
72, 4, 6syl2anb 465 . . 3
8 eldif 3162 . . 3
9 elsn 3655 . . 3
107, 8, 93imtr4i 257 . 2
1110ssriv 3184 1
 Colors of variables: wff set class Syntax hints:   wn 3   wo 357   wa 358   wceq 1623   wcel 1684   cdif 3149   wss 3152  csn 3640  cpr 3641 This theorem is referenced by:  itg11  19046  en2other2  27382  pmtrprfv  27396 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-sn 3646  df-pr 3647
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