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Theorem equsb3lem 1901
Description: Lemma for equsb3 1902. (Contributed by NM, 4-Dec-2005.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)
Assertion
Ref Expression
equsb3lem  |-  ( [ y  /  x ]
x  =  z  <->  y  =  z )
Distinct variable groups:    x, z    x, y

Proof of Theorem equsb3lem
StepHypRef Expression
1 ax-17 1491 . 2  |-  ( y  =  z  ->  A. x  y  =  z )
2 equequ1 1673 . 2  |-  ( x  =  y  ->  (
x  =  z  <->  y  =  z ) )
31, 2sbieh 1748 1  |-  ( [ y  /  x ]
x  =  z  <->  y  =  z )
Colors of variables: wff set class
Syntax hints:    <-> wb 104    = wceq 1316   [wsb 1720
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499
This theorem depends on definitions:  df-bi 116  df-sb 1721
This theorem is referenced by:  equsb3  1902
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