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Theorem raleqbii 2330
 Description: Equality deduction for restricted universal quantifier, changing both formula and quantifier domain. Inference form. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
raleqbii.1 A = B
raleqbii.2 (ψχ)
Assertion
Ref Expression
raleqbii (x A ψx B χ)

Proof of Theorem raleqbii
StepHypRef Expression
1 raleqbii.1 . . . 4 A = B
21eleq2i 2101 . . 3 (x Ax B)
3 raleqbii.2 . . 3 (ψχ)
42, 3imbi12i 228 . 2 ((x Aψ) ↔ (x Bχ))
54ralbii2 2328 1 (x A ψx B χ)
 Colors of variables: wff set class Syntax hints:   ↔ wb 98   = wceq 1242   ∈ wcel 1390  ∀wral 2300 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-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-clel 2033  df-ral 2305 This theorem is referenced by: (None)
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