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Theorem iuneq12daf 28170
 Description: Equality deduction for indexed union, deduction version. (Contributed by Thierry Arnoux, 13-Mar-2017.)
Hypotheses
Ref Expression
iuneq12daf.1
iuneq12daf.2
iuneq12daf.3
iuneq12daf.4
iuneq12daf.5
Assertion
Ref Expression
iuneq12daf

Proof of Theorem iuneq12daf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 iuneq12daf.1 . . . . 5
2 iuneq12daf.5 . . . . . 6
32eleq2d 2514 . . . . 5
41, 3rexbida 2896 . . . 4
5 iuneq12daf.4 . . . . 5
6 iuneq12daf.2 . . . . . 6
7 iuneq12daf.3 . . . . . 6
86, 7rexeqf 2984 . . . . 5
95, 8syl 17 . . . 4
104, 9bitrd 257 . . 3
1110alrimiv 1773 . 2
12 abbi 2565 . . 3
13 df-iun 4280 . . . 4
14 df-iun 4280 . . . 4
1513, 14eqeq12i 2465 . . 3
1612, 15bitr4i 256 . 2
1711, 16sylib 200 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   wa 371  wal 1442   wceq 1444  wnf 1667   wcel 1887  cab 2437  wnfc 2579  wrex 2738  ciun 4278 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-rex 2743  df-iun 4280 This theorem is referenced by:  measvunilem0  29035
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