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Theorem eqsb3lem 2118
 Description: Lemma for eqsb3 2119. (Contributed by Rodolfo Medina, 28-Apr-2010.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)
Assertion
Ref Expression
eqsb3lem ([x / y]y = Ax = A)
Distinct variable groups:   x,y   y,A
Allowed substitution hint:   A(x)

Proof of Theorem eqsb3lem
StepHypRef Expression
1 nfv 1398 . 2 y x = A
2 eqeq1 2024 . 2 (y = x → (y = Ax = A))
31, 2sbie 1652 1 ([x / y]y = Ax = A)
 Colors of variables: wff set class Syntax hints:   ↔ wb 98   = wceq 1226  [wsb 1623 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1312  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-ext 2000 This theorem depends on definitions:  df-bi 110  df-nf 1326  df-sb 1624  df-cleq 2011 This theorem is referenced by:  eqsb3  2119
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