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Theorem cbvrexv 2503
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 1394 . 2 yφ
2 nfv 1394 . 2 xψ
3 cbvralv.1 . 2 (x = y → (φψ))
41, 2, 3cbvrex 2499 1 (x A φy A ψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wrex 2276
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 614  ax-5 1309  ax-7 1310  ax-gen 1311  ax-ie1 1355  ax-ie2 1356  ax-8 1368  ax-10 1369  ax-11 1370  ax-i12 1371  ax-bnd 1372  ax-4 1373  ax-17 1392  ax-i9 1396  ax-ial 1400  ax-i5r 1401  ax-ext 1995
This theorem depends on definitions:  df-bi 110  df-nf 1323  df-sb 1619  df-cleq 2006  df-clel 2009  df-nfc 2140  df-rex 2281
This theorem is referenced by:  cbvrex2v  2511  reu7  2704  reusv3  4130  funcnvuni  4882  fun11iun  5060  fvelimab  5142  fliftfun  5349  grpridd  5608  frecsuc  5895  nnaordex  5999  prarloclemlo  6334  prarloclem3  6337  bj-nn0sucALT  8358
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