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Theorem csbie2t 2894
 Description: Conversion of implicit substitution to explicit substitution into a class (closed form of csbie2 2895). (Contributed by NM, 3-Sep-2007.) (Revised by Mario Carneiro, 13-Oct-2016.)
Hypotheses
Ref Expression
csbie2t.1
csbie2t.2
Assertion
Ref Expression
csbie2t
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem csbie2t
StepHypRef Expression
1 nfa1 1434 . 2
2 nfcvd 2179 . 2
3 csbie2t.1 . . 3
43a1i 9 . 2
5 nfa2 1471 . . . 4
6 nfv 1421 . . . 4
75, 6nfan 1457 . . 3
8 nfcvd 2179 . . 3
9 csbie2t.2 . . . 4
109a1i 9 . . 3
11 sp 1401 . . . . 5
1211sps 1430 . . . 4
1312impl 362 . . 3
147, 8, 10, 13csbiedf 2887 . 2
151, 2, 4, 14csbiedf 2887 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97  wal 1241   wceq 1243   wcel 1393  cvv 2557  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:  csbie2  2895
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