Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  recsfval Unicode version

Theorem recsfval 6221
 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 6211 . 2 recs
2 tfrlem.1 . . 3
32unieqi 3755 . 2
41, 3eqtr4i 2164 1 recs
 Colors of variables: wff set class Syntax hints:   wa 103   wceq 1332  cab 2126  wral 2417  wrex 2418  cuni 3745  con0 4294   cres 4550   wfn 5127  cfv 5132  recscrecs 6210 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rex 2423  df-uni 3746  df-recs 6211 This theorem is referenced by:  tfrlem6  6222  tfrlem7  6223  tfrlem8  6224  tfrlem9  6225  tfrlemibfn  6234  tfrlemiubacc  6236  tfrlemi14d  6239  tfrexlem  6240
 Copyright terms: Public domain W3C validator