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Theorem ddifss 3253
 Description: Double complement under universal class. In classical logic (or given an additional hypothesis, as in ddifnel 3146), this is equality rather than subset. (Contributed by Jim Kingdon, 24-Jul-2018.)
Assertion
Ref Expression
ddifss

Proof of Theorem ddifss
StepHypRef Expression
1 ssv 3061 . 2
2 ssddif 3249 . 2
31, 2mpbi 144 1
 Colors of variables: wff set class Syntax hints:  cvv 2633   cdif 3010   wss 3013 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 582  ax-in2 583  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077 This theorem depends on definitions:  df-bi 116  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-v 2635  df-dif 3015  df-in 3019  df-ss 3026 This theorem is referenced by:  ssindif0im  3361  difdifdirss  3386
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