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Theorem eqsb3lem 2536
Description: Lemma for eqsb3 2537. (Contributed by Rodolfo Medina, 28-Apr-2010.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)
Assertion
Ref Expression
eqsb3lem  |-  ( [ x  /  y ] y  =  A  <->  x  =  A )
Distinct variable groups:    x, y    y, A
Allowed substitution hint:    A( x)

Proof of Theorem eqsb3lem
StepHypRef Expression
1 nfv 1629 . 2  |-  F/ y  x  =  A
2 eqeq1 2442 . 2  |-  ( y  =  x  ->  (
y  =  A  <->  x  =  A ) )
31, 2sbie 2149 1  |-  ( [ x  /  y ] y  =  A  <->  x  =  A )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    = wceq 1652   [wsb 1658
This theorem is referenced by:  eqsb3  2537
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-cleq 2429
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