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Theorem disjiunOLD 4443
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:   , ,   ,   , ,   , ,

Proof of Theorem disjiunOLD
StepHypRef Expression
1 dfdisj2 4424 . 2
2 disjiun 4442 . 2
31, 2sylanbr 473 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  /\w3a 973  A.wal 1393  =wceq 1395  e.wcel 1818  E*wmo 2283  i^icin 3474  C_wss 3475   c0 3784  U_ciun 4330  Disj_wdisj 4422
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rmo 2815  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785  df-iun 4332  df-disj 4423
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