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Theorem csbexg 3261
 Description: The existence of proper substitution into a class. (Contributed by NM, 10-Nov-2005.)
Assertion
Ref Expression
csbexg

Proof of Theorem csbexg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-csb 3252 . 2
2 abid2 2553 . . . . . . 7
3 elex 2964 . . . . . . 7
42, 3syl5eqel 2520 . . . . . 6
54alimi 1568 . . . . 5
6 spsbc 3173 . . . . 5
75, 6syl5 30 . . . 4
87imp 419 . . 3
9 nfcv 2572 . . . . 5
109sbcabel 3238 . . . 4
1110adantr 452 . . 3
128, 11mpbid 202 . 2
131, 12syl5eqel 2520 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549   wcel 1725  cab 2422  cvv 2956  wsbc 3161  csb 3251 This theorem is referenced by:  csbex  3262  issubc  14035  itgparts  19931  abfmpeld  24066  abfmpel  24067  unirep  26414  cdlemk40  31714 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-sbc 3162  df-csb 3252
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