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Theorem eqsb3lem 2137
Description: Lemma for eqsb3 2138. (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 1418 . 2 y x = A
2 eqeq1 2043 . 2 (y = x → (y = Ax = A))
31, 2sbie 1671 1 ([x / y]y = Ax = A)
Colors of variables: wff set class
Syntax hints:  wb 98   = wceq 1242  [wsb 1642
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 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-cleq 2030
This theorem is referenced by:  eqsb3  2138
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