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Theorem csbnestgf 2898
 Description: Nest the composition of two substitutions. (Contributed by NM, 23-Nov-2005.) (Proof shortened by Mario Carneiro, 10-Nov-2016.)
Assertion
Ref Expression
csbnestgf

Proof of Theorem csbnestgf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elex 2566 . . 3
2 df-csb 2853 . . . . . . 7
32abeq2i 2148 . . . . . 6
43sbcbii 2818 . . . . 5
5 nfcr 2170 . . . . . . 7
65alimi 1344 . . . . . 6
7 sbcnestgf 2897 . . . . . 6
86, 7sylan2 270 . . . . 5
94, 8syl5bb 181 . . . 4
109abbidv 2155 . . 3
111, 10sylan 267 . 2
12 df-csb 2853 . 2
13 df-csb 2853 . 2
1411, 12, 133eqtr4g 2097 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  wal 1241   wceq 1243  wnf 1349   wcel 1393  cab 2026  wnfc 2165  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-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:  csbnestg  2900  csbnest1g  2901
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