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Theorem equsb3lem 1867
Description: Lemma for equsb3 1868. (Contributed by NM, 4-Dec-2005.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)
Assertion
Ref Expression
equsb3lem  |-  ( [ x  /  y ] y  =  z  <->  x  =  z )
Distinct variable groups:    y, z    x, y

Proof of Theorem equsb3lem
StepHypRef Expression
1 ax-17 1460 . 2  |-  ( x  =  z  ->  A. y  x  =  z )
2 equequ1 1640 . 2  |-  ( y  =  x  ->  (
y  =  z  <->  x  =  z ) )
31, 2sbieh 1715 1  |-  ( [ x  /  y ] y  =  z  <->  x  =  z )
Colors of variables: wff set class
Syntax hints:    <-> wb 103    = wceq 1285   [wsb 1687
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-sb 1688
This theorem is referenced by:  equsb3  1868
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