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Theorem eqsb3lem 2725
Description: Lemma for eqsb3 2726. (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 1841 . 2 𝑦 𝑥 = 𝐴
2 eqeq1 2624 . 2 (𝑦 = 𝑥 → (𝑦 = 𝐴𝑥 = 𝐴))
31, 2sbie 2406 1 ([𝑥 / 𝑦]𝑦 = 𝐴𝑥 = 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wb 196   = wceq 1481  [wsb 1878
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-10 2017  ax-12 2045  ax-13 2244  ax-ext 2600
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1703  df-nf 1708  df-sb 1879  df-cleq 2613
This theorem is referenced by:  eqsb3  2726
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