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Theorem cbvrabv 2858
 Description: Rule to change the bound variable in a restricted class abstraction, using implicit substitution. (Contributed by NM, 26-May-1999.)
Hypothesis
Ref Expression
cbvrabv.1 (x = y → (φψ))
Assertion
Ref Expression
cbvrabv {x A φ} = {y A ψ}
Distinct variable groups:   x,y,A   φ,y   ψ,x
Allowed substitution hints:   φ(x)   ψ(y)

Proof of Theorem cbvrabv
StepHypRef Expression
1 nfcv 2489 . 2 xA
2 nfcv 2489 . 2 yA
3 nfv 1619 . 2 yφ
4 nfv 1619 . 2 xψ
5 cbvrabv.1 . 2 (x = y → (φψ))
61, 2, 3, 4, 5cbvrab 2857 1 {x A φ} = {y A ψ}
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   = wceq 1642  {crab 2618 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-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rab 2623 This theorem is referenced by: (None)
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