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Theorem csbnest1g 3845
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 3450 . . . 4
21ax-gen 1618 . . 3
3 csbnestgf 3840 . . 3
42, 3mpan2 671 . 2
5 csbco 3444 . . 3
65csbeq2i 3836 . 2
7 csbco 3444 . 2
84, 6, 73eqtr3g 2521 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  A.wal 1393  =wceq 1395  e.wcel 1818  F/_wnfc 2605  [_csb 3434
This theorem is referenced by:  csbidm  3846  csbidmgOLD  3847
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-sbc 3328  df-csb 3435
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