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Theorem equsb3lem 2040
Description: Lemma for equsb3 2041. (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 1605 . 2  |-  F/ y  x  =  z
2 equequ1 1649 . 2  |-  ( y  =  x  ->  (
y  =  z  <->  x  =  z ) )
31, 2sbie 1983 1  |-  ( [ x  /  y ] y  =  z  <->  x  =  z )
Colors of variables: wff set class
Syntax hints:    <-> wb 176   [wsb 1630
This theorem is referenced by:  equsb3  2041
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1636  ax-8 1644  ax-6 1704  ax-7 1709  ax-11 1716  ax-12 1868
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1631
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