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Theorem iuneq12daf 24038
 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 2509 . . . . 5
41, 3rexbida 2726 . . . 4
5 iuneq12daf.4 . . . . 5
6 iuneq12daf.2 . . . . . 6
7 iuneq12daf.3 . . . . . 6
86, 7rexeqf 2907 . . . . 5
95, 8syl 16 . . . 4
104, 9bitrd 246 . . 3
1110alrimiv 1642 . 2
12 abbi 2552 . . 3
13 df-iun 4119 . . . 4
14 df-iun 4119 . . . 4
1513, 14eqeq12i 2455 . . 3
1612, 15bitr4i 245 . 2
1711, 16sylib 190 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550  wnf 1554   wceq 1653   wcel 1727  cab 2428  wnfc 2565  wrex 2712  ciun 4117 This theorem is referenced by:  measvunilem0  24598 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-rex 2717  df-iun 4119
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