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Theorem csbid 3164
 Description: Analog of sbid 1927 for proper substitution into a class. (Contributed by NM, 10-Nov-2005.)
Assertion
Ref Expression
csbid

Proof of Theorem csbid
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-csb 3158 . 2
2 sbsbc 3071 . . . 4
3 sbid 1927 . . . 4
42, 3bitr3i 242 . . 3
54abbii 2470 . 2
6 abid2 2475 . 2
71, 5, 63eqtri 2382 1
 Colors of variables: wff set class Syntax hints:   wceq 1642  wsb 1648   wcel 1710  cab 2344  wsbc 3067  csb 3157 This theorem is referenced by:  csbeq1a  3165  fvmpt2i  5690  disji2f  23218  disjif2  23222  disjabrex  23223  disjabrexf  23224  fvmpt2f  23275  measiuns  23835  fphpd  26222 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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 1930  ax-ext 2339 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-sbc 3068  df-csb 3158
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