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Theorem frforeq3 4110
 Description: Equality theorem for the well-founded predicate. (Contributed by Jim Kingdon, 22-Sep-2021.)
Assertion
Ref Expression
frforeq3 FrFor FrFor

Proof of Theorem frforeq3
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eleq2 2143 . . . . . . 7
21imbi2d 228 . . . . . 6
32ralbidv 2369 . . . . 5
4 eleq2 2143 . . . . 5
53, 4imbi12d 232 . . . 4
65ralbidv 2369 . . 3
7 sseq2 3022 . . 3
86, 7imbi12d 232 . 2
9 df-frfor 4094 . 2 FrFor
10 df-frfor 4094 . 2 FrFor
118, 9, 103bitr4g 221 1 FrFor FrFor
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   wceq 1285   wcel 1434  wral 2349   wss 2974   class class class wbr 3793  FrFor wfrfor 4090 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-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-ral 2354  df-in 2980  df-ss 2987  df-frfor 4094 This theorem is referenced by:  frind  4115
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