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Theorem tfrlem6 7070
Description: Lemma for transfinite recursion. The union of all acceptable functions is a relation. (Contributed by NM, 8-Aug-1994.) (Revised by Mario Carneiro, 9-May-2015.)
Hypothesis
Ref Expression
tfrlem.1
Assertion
Ref Expression
tfrlem6
Distinct variable group:   , , ,

Proof of Theorem tfrlem6
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 reluni 5130 . . 3
2 tfrlem.1 . . . . 5
32tfrlem4 7067 . . . 4
4 funrel 5610 . . . 4
53, 4syl 16 . . 3
61, 5mprgbir 2821 . 2
72recsfval 7069 . . 3
87releqi 5091 . 2
96, 8mpbir 209 1
Colors of variables: wff setvar class
Syntax hints:  /\wa 369  =wceq 1395  e.wcel 1818  {cab 2442  A.wral 2807  E.wrex 2808  U.cuni 4249   con0 4883  |`cres 5006  Relwrel 5009  Funwfun 5587  Fnwfn 5588  `cfv 5593  recscrecs 7060
This theorem is referenced by:  tfrlem7  7071  tfrlem11  7076  tfrlem15  7080  tfrlem16  7081
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-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-iun 4332  df-br 4453  df-opab 4511  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-res 5016  df-iota 5556  df-fun 5595  df-fn 5596  df-fv 5601  df-recs 7061
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