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Theorem bdcuni 7250
Description: The union of a setvar is a bounded class. (Contributed by BJ, 15-Oct-2019.)
Assertion
Ref Expression
bdcuni BOUNDED x

Proof of Theorem bdcuni
Dummy variables y z are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ax-bdel 7195 . . . . 5 BOUNDED y z
21ax-bdex 7193 . . . 4 BOUNDED z x y z
32bdcab 7223 . . 3 BOUNDED {yz x y z}
4 df-rex 2290 . . . . 5 (z x y zz(z x y z))
5 exancom 1481 . . . . 5 (z(z x y z) ↔ z(y z z x))
64, 5bitri 173 . . . 4 (z x y zz(y z z x))
76abbii 2135 . . 3 {yz x y z} = {yz(y z z x)}
83, 7bdceqi 7217 . 2 BOUNDED {yz(y z z x)}
9 df-uni 3555 . 2 x = {yz(y z z x)}
108, 9bdceqir 7218 1 BOUNDED x
Colors of variables: wff set class
Syntax hints:   wa 97  wex 1362  {cab 2008  wrex 2285   cuni 3554  BOUNDED wbdc 7214
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-11 1378  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004  ax-bd0 7187  ax-bdex 7193  ax-bdel 7195  ax-bdsb 7196
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-rex 2290  df-uni 3555  df-bdc 7215
This theorem is referenced by:  bj-uniex2  7286
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