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Theorem tfrlem3-2 5927
 Description: Lemma for transfinite recursion which changes a bound variable (Contributed by Jim Kingdon, 17-Apr-2019.)
Hypothesis
Ref Expression
tfrlem3-2.1 (Fun 𝐹 ∧ (𝐹𝑥) ∈ V)
Assertion
Ref Expression
tfrlem3-2 (Fun 𝐹 ∧ (𝐹𝑔) ∈ V)
Distinct variable group:   𝑥,𝑔,𝐹

Proof of Theorem tfrlem3-2
StepHypRef Expression
1 fveq2 5178 . . . 4 (𝑥 = 𝑔 → (𝐹𝑥) = (𝐹𝑔))
21eleq1d 2106 . . 3 (𝑥 = 𝑔 → ((𝐹𝑥) ∈ V ↔ (𝐹𝑔) ∈ V))
32anbi2d 437 . 2 (𝑥 = 𝑔 → ((Fun 𝐹 ∧ (𝐹𝑥) ∈ V) ↔ (Fun 𝐹 ∧ (𝐹𝑔) ∈ V)))
4 tfrlem3-2.1 . 2 (Fun 𝐹 ∧ (𝐹𝑥) ∈ V)
53, 4chvarv 1812 1 (Fun 𝐹 ∧ (𝐹𝑔) ∈ V)
 Colors of variables: wff set class Syntax hints:   ∧ wa 97   = wceq 1243   ∈ wcel 1393  Vcvv 2557  Fun wfun 4896  ‘cfv 4902 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-iota 4867  df-fv 4910 This theorem is referenced by: (None)
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