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Theorem injust 3326
 Description: Soundness justification theorem for df-in 3327. (Contributed by Rodolfo Medina, 28-Apr-2010.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)
Assertion
Ref Expression
injust
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem injust
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq1 2496 . . . 4
2 eleq1 2496 . . . 4
31, 2anbi12d 692 . . 3
43cbvabv 2555 . 2
5 eleq1 2496 . . . 4
6 eleq1 2496 . . . 4
75, 6anbi12d 692 . . 3
87cbvabv 2555 . 2
94, 8eqtri 2456 1
 Colors of variables: wff set class Syntax hints:   wa 359   wceq 1652   wcel 1725  cab 2422 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 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432
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