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Theorem csbiedf 2887
 Description: Conversion of implicit substitution to explicit substitution into a class. (Contributed by Mario Carneiro, 13-Oct-2016.)
Hypotheses
Ref Expression
csbiedf.1
csbiedf.2
csbiedf.3
csbiedf.4
Assertion
Ref Expression
csbiedf
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem csbiedf
StepHypRef Expression
1 csbiedf.1 . . 3
2 csbiedf.4 . . . 4
32ex 108 . . 3
41, 3alrimi 1415 . 2
5 csbiedf.3 . . 3
6 csbiedf.2 . . 3
7 csbiebt 2886 . . 3
85, 6, 7syl2anc 391 . 2
94, 8mpbid 135 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  wal 1241   wceq 1243  wnf 1349   wcel 1393  wnfc 2165  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-3an 887  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:  csbied  2892  csbie2t  2894
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