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Theorem tfrlem3-2 5868
 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 5121 . . . 4 (x = g → (𝐹x) = (𝐹g))
21eleq1d 2103 . . 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 1809 1 (Fun 𝐹 (𝐹g) V)
 Colors of variables: wff set class Syntax hints:   ∧ wa 97   = wceq 1242   ∈ wcel 1390  Vcvv 2551  Fun wfun 4839  ‘cfv 4845 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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-uni 3572  df-br 3756  df-iota 4810  df-fv 4853 This theorem is referenced by: (None)
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