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Theorem pwjust 3360
 Description: Soundness justification theorem for df-pw 3361. (Contributed by Rodolfo Medina, 28-Apr-2010.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
pwjust
Distinct variable groups:   ,   ,

Proof of Theorem pwjust
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sseq1 2966 . . 3
21cbvabv 2161 . 2
3 sseq1 2966 . . 3
43cbvabv 2161 . 2
52, 4eqtri 2060 1
 Colors of variables: wff set class Syntax hints:   wceq 1243  cab 2026   wss 2917 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-in 2924  df-ss 2931 This theorem is referenced by: (None)
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