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Theorem frrlem5d 25589
 Description: Lemma for founded recursion. The domain of the union of a subset of is a subset of . (Contributed by Paul Chapman, 29-Apr-2012.)
Hypotheses
Ref Expression
frrlem5.1
frrlem5.2 Se
frrlem5.3
Assertion
Ref Expression
frrlem5d
Distinct variable groups:   ,,,   ,,,   ,,,   ,
Allowed substitution hints:   (,)   (,,)

Proof of Theorem frrlem5d
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dmuni 5079 . 2
2 ssel 3342 . . . . 5
3 frrlem5.3 . . . . . 6
43frrlem3 25584 . . . . 5
52, 4syl6 31 . . . 4
65ralrimiv 2788 . . 3
7 iunss 4132 . . 3
86, 7sylibr 204 . 2
91, 8syl5eqss 3392 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   w3a 936  wex 1550   wceq 1652   wcel 1725  cab 2422  wral 2705   wss 3320  cuni 4015  ciun 4093   wfr 4538   Se wse 4539   cdm 4878   cres 4880   wfn 5449  cfv 5454  (class class class)co 6081  cpred 25438 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 2417 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-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-iun 4095  df-br 4213  df-opab 4267  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891  df-iota 5418  df-fun 5456  df-fn 5457  df-fv 5462  df-ov 6084  df-pred 25439
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