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Theorem frrlem5d 29362
 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 5198 . 2
2 ssel 3480 . . . . 5
3 frrlem5.3 . . . . . 6
43frrlem3 29357 . . . . 5
52, 4syl6 33 . . . 4
65ralrimiv 2853 . . 3
7 iunss 4352 . . 3
86, 7sylibr 212 . 2
91, 8syl5eqss 3530 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   w3a 972   wceq 1381  wex 1597   wcel 1802  cab 2426  wral 2791   wss 3458  cuni 4230  ciun 4311   wfr 4821   Se wse 4822   cdm 4985   cres 4987   wfn 5569  cfv 5574  (class class class)co 6277  cpred 29211 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1603  ax-4 1616  ax-5 1689  ax-6 1732  ax-7 1774  ax-10 1821  ax-11 1826  ax-12 1838  ax-13 1983  ax-ext 2419 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 974  df-tru 1384  df-ex 1598  df-nf 1602  df-sb 1725  df-clab 2427  df-cleq 2433  df-clel 2436  df-nfc 2591  df-ral 2796  df-rex 2797  df-rab 2800  df-v 3095  df-dif 3461  df-un 3463  df-in 3465  df-ss 3472  df-nul 3768  df-if 3923  df-sn 4011  df-pr 4013  df-op 4017  df-uni 4231  df-iun 4313  df-br 4434  df-opab 4492  df-xp 4991  df-rel 4992  df-cnv 4993  df-co 4994  df-dm 4995  df-rn 4996  df-res 4997  df-ima 4998  df-iota 5537  df-fun 5576  df-fn 5577  df-fv 5582  df-ov 6280  df-pred 29212 This theorem is referenced by: (None)
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