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Theorem pwjust 3792
 Description: Soundness justification theorem for df-pw 3793. (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 3361 . . 3
21cbvabv 2554 . 2
3 sseq1 3361 . . 3
43cbvabv 2554 . 2
52, 4eqtri 2455 1
 Colors of variables: wff set class Syntax hints:   wceq 1652  cab 2421   wss 3312 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-in 3319  df-ss 3326
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