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Theorem cbvraldva 2841
 Description: Rule used to change the bound variable in a restricted universal 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
cbvraldva (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 cbvraldva
StepHypRef Expression
1 cbvraldva.1 . 2 ((φ x = y) → (ψχ))
2 eqidd 2354 . 2 ((φ x = y) → A = A)
31, 2cbvraldva2 2839 1 (φ → (x A ψy A χ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358  ∀wral 2614 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-cleq 2346  df-clel 2349  df-ral 2619 This theorem is referenced by: (None)
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