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Theorem tfr1onlemssrecs 6236
 Description: Lemma for tfr1on 6247. The union of functions acceptable for tfr1on 6247 is a subset of recs. (Contributed by Jim Kingdon, 15-Mar-2022.)
Hypotheses
Ref Expression
tfr1onlemssrecs.1
tfr1onlemssrecs.x
Assertion
Ref Expression
tfr1onlemssrecs recs
Distinct variable groups:   ,,,   ,   ,
Allowed substitution hints:   (,)   (,,)   (,)

Proof of Theorem tfr1onlemssrecs
StepHypRef Expression
1 tfr1onlemssrecs.1 . . . 4
2 tfr1onlemssrecs.x . . . . . 6
3 ordsson 4408 . . . . . 6
4 ssrexv 3162 . . . . . 6
52, 3, 43syl 17 . . . . 5
65ss2abdv 3170 . . . 4
71, 6eqsstrid 3143 . . 3
87unissd 3760 . 2
9 df-recs 6202 . 2 recs
108, 9sseqtrrdi 3146 1 recs
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1331  cab 2125  wral 2416  wrex 2417   wss 3071  cuni 3736   word 4284  con0 4285   cres 4541   wfn 5118  cfv 5123  recscrecs 6201 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-in 3077  df-ss 3084  df-uni 3737  df-tr 4027  df-iord 4288  df-on 4290  df-recs 6202 This theorem is referenced by:  tfr1onlembfn  6241  tfr1onlemubacc  6243  tfr1onlemres  6246
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