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Theorem eqsb3lem 2383
Description: Lemma for eqsb3 2384. (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 1605 . 2  |-  F/ y  x  =  A
2 eqeq1 2289 . 2  |-  ( y  =  x  ->  (
y  =  A  <->  x  =  A ) )
31, 2sbie 1978 1  |-  ( [ x  /  y ] y  =  A  <->  x  =  A )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    = wceq 1623   [wsb 1629
This theorem is referenced by:  eqsb3  2384
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 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-cleq 2276
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