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Theorem difpr 3671
 Description: Removing two elements as pair of elements corresponds to removing each of the two elements as singletons. (Contributed by Alexander van der Vekens, 13-Jul-2018.)
Assertion
Ref Expression
difpr

Proof of Theorem difpr
StepHypRef Expression
1 df-pr 3540 . . 3
21difeq2i 3197 . 2
3 difun1 3342 . 2
42, 3eqtri 2161 1
 Colors of variables: wff set class Syntax hints:   wceq 1332   cdif 3074   cun 3075  csn 3533  cpr 3534 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rab 2426  df-v 2692  df-dif 3079  df-un 3081  df-in 3083  df-pr 3540 This theorem is referenced by:  hashdifpr  10618
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