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Theorem cbvrexv 2836
 Description: Change the bound variable of a restricted existential quantifier using implicit substitution. (Contributed by NM, 2-Jun-1998.)
Hypothesis
Ref Expression
cbvralv.1 (x = y → (φψ))
Assertion
Ref Expression
cbvrexv (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 cbvrexv
StepHypRef Expression
1 nfv 1619 . 2 yφ
2 nfv 1619 . 2 xψ
3 cbvralv.1 . 2 (x = y → (φψ))
41, 2, 3cbvrex 2832 1 (x A φy A ψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∃wrex 2615 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  df-rex 2620 This theorem is referenced by:  cbvrex2v  2844  reu7  3031  ncfinraise  4481  ncfinlower  4483  nnpw1ex  4484  nnpweq  4523  vfinspss  4551  funcnvuni  5161  fun11iun  5305  clos1basesuc  5882  ncspw1eu  6159  nncdiv3  6277
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