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Theorem uniintab 4080
 Description: The union and the intersection of a class abstraction are equal exactly when there is a unique satisfying value of . (Contributed by Mario Carneiro, 24-Dec-2016.)
Assertion
Ref Expression
uniintab

Proof of Theorem uniintab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 euabsn2 3867 . 2
2 uniintsn 4079 . 2
31, 2bitr4i 244 1
 Colors of variables: wff set class Syntax hints:   wb 177  wex 1550   wceq 1652  weu 2280  cab 2421  csn 3806  cuni 4007  cint 4042 This theorem is referenced by:  iotaint  5423 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-sn 3812  df-pr 3813  df-uni 4008  df-int 4043
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