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Theorem csbing 3144
 Description: Distribute proper substitution through an intersection relation. (Contributed by Alan Sare, 22-Jul-2012.)
Assertion
Ref Expression
csbing

Proof of Theorem csbing
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbeq1 2855 . . 3
2 csbeq1 2855 . . . 4
3 csbeq1 2855 . . . 4
42, 3ineq12d 3139 . . 3
51, 4eqeq12d 2054 . 2
6 vex 2560 . . 3
7 nfcsb1v 2882 . . . 4
8 nfcsb1v 2882 . . . 4
97, 8nfin 3143 . . 3
10 csbeq1a 2860 . . . 4
11 csbeq1a 2860 . . . 4
1210, 11ineq12d 3139 . . 3
136, 9, 12csbief 2891 . 2
145, 13vtoclg 2613 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1243   wcel 1393  csb 2852   cin 2916 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-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rab 2315  df-v 2559  df-sbc 2765  df-csb 2853  df-in 2924 This theorem is referenced by:  csbresg  4615
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