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Theorem snjust 3740
 Description: Soundness justification theorem for df-sn 3741. (Contributed by Rodolfo Medina, 28-Apr-2010.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
snjust {x x = A} = {y y = A}
Distinct variable groups:   x,A   y,A

Proof of Theorem snjust
Dummy variable z is distinct from all other variables.
StepHypRef Expression
1 eqeq1 2359 . . 3 (x = z → (x = Az = A))
21cbvabv 2472 . 2 {x x = A} = {z z = A}
3 eqeq1 2359 . . 3 (z = y → (z = Ay = A))
43cbvabv 2472 . 2 {z z = A} = {y y = A}
52, 4eqtri 2373 1 {x x = A} = {y y = A}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642  {cab 2339 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346 This theorem is referenced by: (None)
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