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Theorem uniqs 6956
 Description: The union of a quotient set. (Contributed by NM, 9-Dec-2008.)
Assertion
Ref Expression
uniqs

Proof of Theorem uniqs
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ecexg 6901 . . . . 5
21ralrimivw 2782 . . . 4
3 dfiun2g 4115 . . . 4
42, 3syl 16 . . 3
54eqcomd 2440 . 2
6 df-qs 6903 . . 3
76unieqi 4017 . 2
8 df-ec 6899 . . . . 5
98a1i 11 . . . 4
109iuneq2i 4103 . . 3
11 imaiun 5984 . . 3
12 iunid 4138 . . . 4
1312imaeq2i 5193 . . 3
1410, 11, 133eqtr2ri 2462 . 2
155, 7, 143eqtr4g 2492 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  cab 2421  wral 2697  wrex 2698  cvv 2948  csn 3806  cuni 4007  ciun 4085  cima 4873  cec 6895  cqs 6896 This theorem is referenced by:  uniqs2  6958  ecqs  6960 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395  ax-un 4693 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-iun 4087  df-br 4205  df-opab 4259  df-xp 4876  df-cnv 4878  df-dm 4880  df-rn 4881  df-res 4882  df-ima 4883  df-ec 6899  df-qs 6903
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