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Theorem csbexga 3885
 Description: The existence of proper substitution into a class. (Contributed by NM, 10-Nov-2005.)
Assertion
Ref Expression
csbexga

Proof of Theorem csbexga
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-csb 2853 . 2
2 abid2 2158 . . . . . . 7
3 elex 2566 . . . . . . 7
42, 3syl5eqel 2124 . . . . . 6
54alimi 1344 . . . . 5
6 spsbc 2775 . . . . 5
75, 6syl5 28 . . . 4
87imp 115 . . 3
9 nfcv 2178 . . . . 5
109sbcabel 2839 . . . 4
1110adantr 261 . . 3
128, 11mpbid 135 . 2
131, 12syl5eqel 2124 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  wal 1241   wcel 1393  cab 2026  cvv 2557  wsbc 2764  csb 2852 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-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-sbc 2765  df-csb 2853 This theorem is referenced by:  csbexa  3886
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