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Theorem equsb3lem 2183
Description: Lemma for equsb3 2184. (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 1630 . 2  |-  F/ y  x  =  z
2 equequ1 1698 . 2  |-  ( y  =  x  ->  (
y  =  z  <->  x  =  z ) )
31, 2sbie 2154 1  |-  ( [ x  /  y ] y  =  z  <->  x  =  z )
Colors of variables: wff set class
Syntax hints:    <-> wb 178   [wsb 1659
This theorem is referenced by:  equsb3  2184
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-11 1763  ax-12 1953
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555  df-sb 1660
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