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Theorem dmuni 4460
 Description: The domain of a union. Part of Exercise 8 of [Enderton] p. 41. (Contributed by NM, 3-Feb-2004.)
Assertion
Ref Expression
dmuni
Distinct variable group:   ,

Proof of Theorem dmuni
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 excom 1527 . . . . 5
2 ancom 253 . . . . . . 7
3 19.41v 1755 . . . . . . 7
4 vex 2529 . . . . . . . . 9
54eldm2 4448 . . . . . . . 8
65anbi2i 430 . . . . . . 7
72, 3, 63bitr4i 201 . . . . . 6
87exbii 1469 . . . . 5
91, 8bitri 173 . . . 4
10 eluni 3546 . . . . 5
1110exbii 1469 . . . 4
12 df-rex 2281 . . . 4
139, 11, 123bitr4i 201 . . 3
144eldm2 4448 . . 3
15 eliun 3624 . . 3
1613, 14, 153bitr4i 201 . 2
1716eqriv 2010 1
 Colors of variables: wff set class Syntax hints:   wa 97   wceq 1223  wex 1354   wcel 1366  wrex 2276  cop 3342  cuni 3543  ciun 3620   cdm 4260 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-io 614  ax-5 1309  ax-7 1310  ax-gen 1311  ax-ie1 1355  ax-ie2 1356  ax-8 1368  ax-10 1369  ax-11 1370  ax-i12 1371  ax-bnd 1372  ax-4 1373  ax-17 1392  ax-i9 1396  ax-ial 1400  ax-i5r 1401  ax-ext 1995 This theorem depends on definitions:  df-bi 110  df-3an 869  df-tru 1226  df-nf 1323  df-sb 1619  df-clab 2000  df-cleq 2006  df-clel 2009  df-nfc 2140  df-ral 2280  df-rex 2281  df-v 2528  df-un 2890  df-sn 3345  df-pr 3346  df-op 3348  df-uni 3544  df-iun 3622  df-br 3728  df-dm 4270 This theorem is referenced by:  tfrlem8  5844  tfrlemi14d  5856  tfrlemi14  5857
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