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Theorem cbvrexv 2528
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 1418 . 2 yφ
2 nfv 1418 . 2 xψ
3 cbvralv.1 . 2 (x = y → (φψ))
41, 2, 3cbvrex 2524 1 (x A φy A ψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wrex 2301
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306
This theorem is referenced by:  cbvrex2v  2536  reu7  2730  reusv3  4158  funcnvuni  4911  fun11iun  5090  fvelimab  5172  fliftfun  5379  grpridd  5639  frecsuc  5930  nnaordex  6036  prarloclemlo  6477  prarloclem3  6480  cauappcvgprlemdisj  6623  cauappcvgprlemladdru  6628  cauappcvgprlemladdrl  6629  cauappcvgpr  6634  caucvgprlemdisj  6645  caucvgprlemcl  6647  caucvgprlemladdfu  6648  caucvgprlemladdrl  6649  caucvgpr  6653  ublbneg  8324  bj-nn0sucALT  9438
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