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Theorem difjust 3324
 Description: Soundness justification theorem for df-dif 3325. (Contributed by Rodolfo Medina, 27-Apr-2010.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)
Assertion
Ref Expression
difjust
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem difjust
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq1 2498 . . . 4
2 eleq1 2498 . . . . 5
32notbid 287 . . . 4
41, 3anbi12d 693 . . 3
54cbvabv 2557 . 2
6 eleq1 2498 . . . 4
7 eleq1 2498 . . . . 5
87notbid 287 . . . 4
96, 8anbi12d 693 . . 3
109cbvabv 2557 . 2
115, 10eqtri 2458 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 360   wceq 1653   wcel 1726  cab 2424 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434
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