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Theorem cbvabv 2158
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 26-May-1999.)
Hypothesis
Ref Expression
cbvabv.1 (x = y → (φψ))
Assertion
Ref Expression
cbvabv {xφ} = {yψ}
Distinct variable groups:   φ,y   ψ,x
Allowed substitution hints:   φ(x)   ψ(y)

Proof of Theorem cbvabv
StepHypRef Expression
1 nfv 1418 . 2 yφ
2 nfv 1418 . 2 xψ
3 cbvabv.1 . 2 (x = y → (φψ))
41, 2, 3cbvab 2157 1 {xφ} = {yψ}
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   = wceq 1242  {cab 2023
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-bnd 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-clab 2024  df-cleq 2030
This theorem is referenced by:  cdeqab1  2750  difjust  2913  unjust  2915  injust  2917  uniiunlem  3022  dfif3  3337  pwjust  3352  snjust  3372  intab  3635  iotajust  4809  tfrlemi1  5887  frecsuc  5930  nqprlu  6529  recexpr  6609  bds  9286
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