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Theorem difjust 2919
 Description: Soundness justification theorem for df-dif 2920. (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 2100 . . . 4
2 eleq1 2100 . . . . 5
32notbid 592 . . . 4
41, 3anbi12d 442 . . 3
54cbvabv 2161 . 2
6 eleq1 2100 . . . 4
7 eleq1 2100 . . . . 5
87notbid 592 . . . 4
96, 8anbi12d 442 . . 3
109cbvabv 2161 . 2
115, 10eqtri 2060 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 97   wceq 1243   wcel 1393  cab 2026 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-in1 544  ax-in2 545  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 This theorem is referenced by: (None)
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