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Theorem eqsb3lem 2220
Description: Lemma for eqsb3 2221. (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 1493 . 2 𝑥 𝑦 = 𝐴
2 eqeq1 2124 . 2 (𝑥 = 𝑦 → (𝑥 = 𝐴𝑦 = 𝐴))
31, 2sbie 1749 1 ([𝑦 / 𝑥]𝑥 = 𝐴𝑦 = 𝐴)
Colors of variables: wff set class
Syntax hints:  wb 104   = wceq 1316  [wsb 1720
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 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-cleq 2110
This theorem is referenced by:  eqsb3  2221
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