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Theorem cbvralv 2835
 Description: Change the bound variable of a restricted universal quantifier using implicit substitution. (Contributed by NM, 28-Jan-1997.)
Hypothesis
Ref Expression
cbvralv.1 (x = y → (φψ))
Assertion
Ref Expression
cbvralv (x A φy A ψ)
Distinct variable groups:   x,A   y,A   φ,y   ψ,x
Allowed substitution hints:   φ(x)   ψ(y)

Proof of Theorem cbvralv
StepHypRef Expression
1 nfv 1619 . 2 yφ
2 nfv 1619 . 2 xψ
3 cbvralv.1 . 2 (x = y → (φψ))
41, 2, 3cbvral 2831 1 (x A φy A ψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀wral 2614 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-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619 This theorem is referenced by:  cbvral2v  2843  cbvral3v  2845  reu7  3031  nndisjeq  4429  evenodddisj  4516  nnadjoin  4520  tfinnn  4534  nnc3n3p1  6278  nchoicelem12  6300  nchoicelem17  6305
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