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Theorem recsfval 6644
 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 recs
Distinct variable group:   ,,,
Allowed substitution hints:   (,,)

Proof of Theorem recsfval
StepHypRef Expression
1 df-recs 6635 . 2 recs
2 tfrlem.1 . . 3
32unieqi 4027 . 2
41, 3eqtr4i 2461 1 recs
 Colors of variables: wff set class Syntax hints:   wa 360   wceq 1653  cab 2424  wral 2707  wrex 2708  cuni 4017  con0 4583   cres 4882   wfn 5451  cfv 5456  recscrecs 6634 This theorem is referenced by:  tfrlem6  6645  tfrlem7  6646  tfrlem8  6647  tfrlem9  6648  tfrlem9a  6649  tfrlem13  6653 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2713  df-uni 4018  df-recs 6635
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