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Theorem cbvexv 1985
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
cbvalv.1  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
Assertion
Ref Expression
cbvexv  |-  ( E. x ph  <->  E. y ps )
Distinct variable groups:    ph, y    ps, x
Allowed substitution hints:    ph( x)    ps( y)

Proof of Theorem cbvexv
StepHypRef Expression
1 nfv 1629 . 2  |-  F/ y
ph
2 nfv 1629 . 2  |-  F/ x ps
3 cbvalv.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
41, 2, 3cbvex 1983 1  |-  ( E. x ph  <->  E. y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177   E.wex 1550
This theorem is referenced by:  eujust  2282  euind  3113  reuind  3129  cbvopab2v  4274  bm1.3ii  4325  zfun  4694  reusv2lem2  4717  relop  5015  dmcoss  5127  fv3  5736  exfo  5879  ac6sfi  7343  brwdom2  7533  aceq1  7990  aceq0  7991  aceq3lem  7993  dfac4  7995  kmlem2  8023  kmlem13  8034  axdc4lem  8327  zfac  8332  zfcndun  8482  zfcndac  8486  sup2  9956  supmul  9968  climmo  12343  summo  12503  gsumval3eu  15505  elpt  17596  usgraedg4  21398  prodmo  25254  wfrlem1  25530  frrlem1  25574  fdc  26430  ax10ext  27564  fnchoice  27657  bnj1185  29092
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554
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