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Theorem sbequ5 2126
Description: Substitution does not change an identical variable specifier. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbequ5  |-  ( [ w  /  z ] A. x  x  =  y  <->  A. x  x  =  y )

Proof of Theorem sbequ5
StepHypRef Expression
1 nfae 2043 . 2  |-  F/ z A. x  x  =  y
21sbf 2119 1  |-  ( [ w  /  z ] A. x  x  =  y  <->  A. x  x  =  y )
Colors of variables: wff set class
Syntax hints:    <-> wb 178   A.wal 1550   [wsb 1659
This theorem is referenced by:  sbal  2206
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555  df-sb 1660
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