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Theorem frrlem6 30310
 Description: Lemma for founded recursion. The union of all acceptable functions is a relationship. (Contributed by Paul Chapman, 21-Apr-2012.)
Hypotheses
Ref Expression
frrlem6.1
frrlem6.2
Assertion
Ref Expression
frrlem6
Distinct variable groups:   ,,,   ,,,   ,,,
Allowed substitution hints:   (,,)   (,,)

Proof of Theorem frrlem6
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 frrlem6.2 . 2
2 reluni 4976 . . . 4
3 frrlem6.1 . . . . . 6
43frrlem2 30302 . . . . 5
5 funrel 5618 . . . . 5
64, 5syl 17 . . . 4
72, 6mprgbir 2796 . . 3
8 releq 4937 . . 3
97, 8mpbiri 236 . 2
101, 9ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:   wa 370   w3a 982   wceq 1437  wex 1659   wcel 1870  cab 2414  wral 2782   wss 3442  cuni 4222   cres 4856   wrel 4859  cpred 5398   wfun 5595   wfn 5596  cfv 5601  (class class class)co 6305 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ral 2787  df-rex 2788  df-rab 2791  df-v 3089  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3768  df-if 3916  df-sn 4003  df-pr 4005  df-op 4009  df-uni 4223  df-iun 4304  df-br 4427  df-opab 4485  df-xp 4860  df-rel 4861  df-cnv 4862  df-co 4863  df-dm 4864  df-rn 4865  df-res 4866  df-ima 4867  df-pred 5399  df-iota 5565  df-fun 5603  df-fn 5604  df-fv 5609  df-ov 6308 This theorem is referenced by: (None)
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