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Theorem snjust 3372
Description: Soundness justification theorem for df-sn 3373. (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 2043 . . 3 (x = z → (x = Az = A))
21cbvabv 2158 . 2 {xx = A} = {zz = A}
3 eqeq1 2043 . . 3 (z = y → (z = Ay = A))
43cbvabv 2158 . 2 {zz = A} = {yy = A}
52, 4eqtri 2057 1 {xx = A} = {yy = A}
Colors of variables: wff set class
Syntax hints:   = wceq 1242  {cab 2023
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030
This theorem is referenced by: (None)
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