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Theorem snjust 3351
Description: Soundness justification theorem for df-sn 3352. (Contributed by Rodolfo Medina, 28-Apr-2010.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
snjust {xx = A} = {yy = 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 2024 . . 3 (x = z → (x = Az = A))
21cbvabv 2139 . 2 {xx = A} = {zz = A}
3 eqeq1 2024 . . 3 (z = y → (z = Ay = A))
43cbvabv 2139 . 2 {zz = A} = {yy = A}
52, 4eqtri 2038 1 {xx = A} = {yy = A}
Colors of variables: wff set class
Syntax hints:   = wceq 1226  {cab 2004
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-io 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011
This theorem is referenced by: (None)
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