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Theorem disjiunOLD 4195
 Description: A disjoint collection yields disjoint indexed unions for disjoint index sets. (Contributed by Mario Carneiro, 26-Mar-2015.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
disjiunOLD
Distinct variable groups:   ,,   ,   ,,   ,,
Allowed substitution hint:   ()

Proof of Theorem disjiunOLD
StepHypRef Expression
1 dfdisj2 4176 . 2 Disj
2 disjiun 4194 . 2 Disj
31, 2sylanbr 460 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   w3a 936  wal 1549   wceq 1652   wcel 1725  wmo 2281   cin 3311   wss 3312  c0 3620  ciun 4085  Disj wdisj 4174 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 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-rmo 2705  df-v 2950  df-dif 3315  df-in 3319  df-ss 3326  df-nul 3621  df-iun 4087  df-disj 4175
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