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Theorem csbdmg 4529
 Description: Distribute proper substitution through the domain of a class. (Contributed by Jim Kingdon, 8-Dec-2018.)
Assertion
Ref Expression
csbdmg

Proof of Theorem csbdmg
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 csbabg 2907 . . 3
2 sbcex2 2812 . . . . 5
3 sbcel2g 2871 . . . . . 6
43exbidv 1706 . . . . 5
52, 4syl5bb 181 . . . 4
65abbidv 2155 . . 3
71, 6eqtrd 2072 . 2
8 dfdm3 4522 . . 3
98csbeq2i 2876 . 2
10 dfdm3 4522 . 2
117, 9, 103eqtr4g 2097 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1243  wex 1381   wcel 1393  cab 2026  wsbc 2764  csb 2852  cop 3378   cdm 4345 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  df-br 3765  df-dm 4355 This theorem is referenced by:  sbcfng  5044
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