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Theorem cbvrexdva 2534
 Description: Rule used to change the bound variable in a restricted existential quantifier with implicit substitution. Deduction form. (Contributed by David Moews, 1-May-2017.)
Hypothesis
Ref Expression
cbvraldva.1 ((φ x = y) → (ψχ))
Assertion
Ref Expression
cbvrexdva (φ → (x A ψy A χ))
Distinct variable groups:   ψ,y   χ,x   x,A,y   φ,x,y
Allowed substitution hints:   ψ(x)   χ(y)

Proof of Theorem cbvrexdva
StepHypRef Expression
1 cbvraldva.1 . 2 ((φ x = y) → (ψχ))
2 eqidd 2038 . 2 ((φ x = y) → A = A)
31, 2cbvrexdva2 2532 1 (φ → (x A ψy A χ))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ↔ wb 98  ∃wrex 2301 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-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-cleq 2030  df-clel 2033  df-rex 2306 This theorem is referenced by:  tfrlem3ag  5865  tfrlem3a  5866  tfrlemi1  5887
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