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Theorem tfrlem3-2 5957
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 5205 . . . 4 (𝑥 = 𝑔 → (𝐹𝑥) = (𝐹𝑔))
21eleq1d 2122 . . 3 (𝑥 = 𝑔 → ((𝐹𝑥) ∈ V ↔ (𝐹𝑔) ∈ V))
32anbi2d 445 . 2 (𝑥 = 𝑔 → ((Fun 𝐹 ∧ (𝐹𝑥) ∈ V) ↔ (Fun 𝐹 ∧ (𝐹𝑔) ∈ V)))
4 tfrlem3-2.1 . 2 (Fun 𝐹 ∧ (𝐹𝑥) ∈ V)
53, 4chvarv 1828 1 (Fun 𝐹 ∧ (𝐹𝑔) ∈ V)
Colors of variables: wff set class
Syntax hints:  wa 101   = wceq 1259  wcel 1409  Vcvv 2574  Fun wfun 4923  cfv 4929
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329  df-v 2576  df-un 2949  df-sn 3408  df-pr 3409  df-op 3411  df-uni 3608  df-br 3792  df-iota 4894  df-fv 4937
This theorem is referenced by: (None)
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