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Theorem frforeq2 4128
 Description: Equality theorem for the well-founded predicate. (Contributed by Jim Kingdon, 22-Sep-2021.)
Assertion
Ref Expression
frforeq2 FrFor FrFor

Proof of Theorem frforeq2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 raleq 2554 . . . . 5
21imbi1d 229 . . . 4
32raleqbi1dv 2562 . . 3
4 sseq1 3029 . . 3
53, 4imbi12d 232 . 2
6 df-frfor 4114 . 2 FrFor
7 df-frfor 4114 . 2 FrFor
85, 6, 73bitr4g 221 1 FrFor FrFor
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   wceq 1285   wcel 1434  wral 2353   wss 2982   class class class wbr 3805  FrFor wfrfor 4110 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-in 2988  df-ss 2995  df-frfor 4114 This theorem is referenced by:  freq2  4129
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