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Theorem equsb3lem 2064
Description: Lemma for equsb3 2065. (Contributed by Raph Levien and FL, 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 nfv 1629 . 2  |-  F/ y  x  =  z
2 equequ1 1829 . 2  |-  ( y  =  x  ->  (
y  =  z  <->  x  =  z ) )
31, 2sbie 1911 1  |-  ( [ x  /  y ] y  =  z  <->  x  =  z )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    = wceq 1619   [wsb 1883
This theorem is referenced by:  equsb3  2065
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-8 1623  ax-17 1628  ax-9 1684  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884
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