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Theorem eqsb3lem 2453
 Description: Lemma for eqsb3 2454. (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 1619 . 2 x y = A
2 eqeq1 2359 . 2 (x = y → (x = Ay = A))
31, 2sbie 2038 1 ([y / x]x = Ay = A)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   = wceq 1642  [wsb 1648 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346 This theorem is referenced by:  eqsb3  2454
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