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Theorem cbvreuv 2837
 Description: Change the bound variable of a restricted uniqueness quantifier using implicit substitution. (Contributed by NM, 5-Apr-2004.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypothesis
Ref Expression
cbvralv.1 (x = y → (φψ))
Assertion
Ref Expression
cbvreuv (∃!x A φ∃!y A ψ)
Distinct variable groups:   x,A   y,A   φ,y   ψ,x
Allowed substitution hints:   φ(x)   ψ(y)

Proof of Theorem cbvreuv
StepHypRef Expression
1 nfv 1619 . 2 yφ
2 nfv 1619 . 2 xψ
3 cbvralv.1 . 2 (x = y → (φψ))
41, 2, 3cbvreu 2833 1 (∃!x A φ∃!y A ψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∃!wreu 2616 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-cleq 2346  df-clel 2349  df-reu 2621 This theorem is referenced by:  reu8  3032
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