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Theorem recsfval 7069
Description: Lemma for transfinite recursion. The definition recs is the union of all acceptable functions. (Contributed by Mario Carneiro, 9-May-2015.)
Hypothesis
Ref Expression
tfrlem.1
Assertion
Ref Expression
recsfval
Distinct variable group:   , , ,

Proof of Theorem recsfval
StepHypRef Expression
1 df-recs 7061 . 2
2 tfrlem.1 . . 3
32unieqi 4258 . 2
41, 3eqtr4i 2489 1
Colors of variables: wff setvar class
Syntax hints:  /\wa 369  =wceq 1395  {cab 2442  A.wral 2807  E.wrex 2808  U.cuni 4249   con0 4883  |`cres 5006  Fnwfn 5588  `cfv 5593  recscrecs 7060
This theorem is referenced by:  tfrlem6  7070  tfrlem7  7071  tfrlem8  7072  tfrlem9  7073  tfrlem9a  7074  tfrlem13  7078
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-an 371  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-rex 2813  df-uni 4250  df-recs 7061
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