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Theorem uniintab 4320
 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 4098 . 2
2 uniintsn 4319 . 2
31, 2bitr4i 252 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wceq 1379  wex 1596  weu 2275  cab 2452  csn 4027  cuni 4245  cint 4282 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2819  df-rex 2820  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-sn 4028  df-pr 4030  df-uni 4246  df-int 4283 This theorem is referenced by:  iotaint  5562
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