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Theorem snjust 3408
 Description: Soundness justification theorem for df-sn 3409. (Contributed by Rodolfo Medina, 28-Apr-2010.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
snjust
Distinct variable groups:   ,   ,

Proof of Theorem snjust
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqeq1 2062 . . 3
21cbvabv 2177 . 2
3 eqeq1 2062 . . 3
43cbvabv 2177 . 2
52, 4eqtri 2076 1
 Colors of variables: wff set class Syntax hints:   wceq 1259  cab 2042 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049 This theorem is referenced by: (None)
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