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Theorem eqsb3lem 2182
Description: Lemma for eqsb3 2183. (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 1462 . 2  |-  F/ y  x  =  A
2 eqeq1 2088 . 2  |-  ( y  =  x  ->  (
y  =  A  <->  x  =  A ) )
31, 2sbie 1715 1  |-  ( [ x  /  y ] y  =  A  <->  x  =  A )
Colors of variables: wff set class
Syntax hints:    <-> wb 103    = wceq 1285   [wsb 1686
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-cleq 2075
This theorem is referenced by:  eqsb3  2183
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