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Theorem csbnest1g 2901
 Description: Nest the composition of two substitutions. (Contributed by NM, 23-May-2006.) (Proof shortened by Mario Carneiro, 11-Nov-2016.)
Assertion
Ref Expression
csbnest1g

Proof of Theorem csbnest1g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfcsb1v 2882 . . . 4
21ax-gen 1338 . . 3
3 csbnestgf 2898 . . 3
42, 3mpan2 401 . 2
5 csbco 2861 . . 3
65csbeq2i 2876 . 2
7 csbco 2861 . 2
84, 6, 73eqtr3g 2095 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1241   wceq 1243   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:  csbidmg  2902
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