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Theorem frrlem7 25557
 Description: Lemma for founded recursion. The domain of is a subclass of . (Contributed by Paul Chapman, 21-Apr-2012.)
Hypotheses
Ref Expression
frrlem6.1
frrlem6.2
Assertion
Ref Expression
frrlem7
Distinct variable groups:   ,,,   ,,,   ,,,
Allowed substitution hints:   (,,)   (,,)

Proof of Theorem frrlem7
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 frrlem6.2 . . . 4
21dmeqi 5063 . . 3
3 dmuni 5071 . . 3
42, 3eqtri 2455 . 2
5 iunss 4124 . . 3
6 frrlem6.1 . . . 4
76frrlem3 25549 . . 3
85, 7mprgbir 2768 . 2
94, 8eqsstri 3370 1
 Colors of variables: wff set class Syntax hints:   wa 359   w3a 936  wex 1550   wceq 1652  cab 2421  wral 2697   wss 3312  cuni 4007  ciun 4085   cdm 4870   cres 4872   wfn 5441  cfv 5446  (class class class)co 6073  cpred 25426 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-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  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-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-res 4882  df-ima 4883  df-iota 5410  df-fun 5448  df-fn 5449  df-fv 5454  df-ov 6076  df-pred 25427
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