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Theorem csbing 3462
 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 3139 . . 3
2 csbeq1 3139 . . . 4
3 csbeq1 3139 . . . 4
42, 3ineq12d 3458 . . 3
51, 4eqeq12d 2367 . 2
6 vex 2862 . . 3
7 nfcsb1v 3168 . . . 4
8 nfcsb1v 3168 . . . 4
97, 8nfin 3230 . . 3
10 csbeq1a 3144 . . . 4
11 csbeq1a 3144 . . . 4
1210, 11ineq12d 3458 . . 3
136, 9, 12csbief 3177 . 2
145, 13vtoclg 2914 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1642   wcel 1710  csb 3136   cin 3208 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-sbc 3047  df-csb 3137  df-nin 3211  df-compl 3212  df-in 3213 This theorem is referenced by:  csbresg  4976
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