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Theorem iunconstm 3656
Description: Indexed union of a constant class, i.e. where B does not depend on x. (Contributed by Jim Kingdon, 15-Aug-2018.)
Assertion
Ref Expression
iunconstm (x x A x A B = B)
Distinct variable groups:   x,A   x,B

Proof of Theorem iunconstm
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 r19.9rmv 3307 . . 3 (x x A → (y Bx A y B))
2 eliun 3652 . . 3 (y x A Bx A y B)
31, 2syl6rbbr 188 . 2 (x x A → (y x A By B))
43eqrdv 2035 1 (x x A x A B = B)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242  wex 1378   wcel 1390  wrex 2301   ciun 3648
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-iun 3650
This theorem is referenced by: (None)
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