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Theorem eqsb3lem 2242
 Description: Lemma for eqsb3 2243. (Contributed by Rodolfo Medina, 28-Apr-2010.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)
Assertion
Ref Expression
eqsb3lem ([𝑦 / 𝑥]𝑥 = 𝐴𝑦 = 𝐴)
Distinct variable groups:   𝑥,𝑦   𝑥,𝐴
Allowed substitution hint:   𝐴(𝑦)

Proof of Theorem eqsb3lem
StepHypRef Expression
1 nfv 1508 . 2 𝑥 𝑦 = 𝐴
2 eqeq1 2146 . 2 (𝑥 = 𝑦 → (𝑥 = 𝐴𝑦 = 𝐴))
31, 2sbie 1764 1 ([𝑦 / 𝑥]𝑥 = 𝐴𝑦 = 𝐴)
 Colors of variables: wff set class Syntax hints:   ↔ wb 104   = wceq 1331  [wsb 1735 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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-cleq 2132 This theorem is referenced by:  eqsb3  2243
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