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Theorem csbnestgf 3184
 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 2867 . . 3
2 df-csb 3137 . . . . . . 7
32abeq2i 2460 . . . . . 6
43sbcbii 3101 . . . . 5
5 nfcr 2481 . . . . . . 7
65alimi 1559 . . . . . 6
7 sbcnestgf 3183 . . . . . 6
86, 7sylan2 460 . . . . 5
94, 8syl5bb 248 . . . 4
109abbidv 2467 . . 3
111, 10sylan 457 . 2
12 df-csb 3137 . 2
13 df-csb 3137 . 2
1411, 12, 133eqtr4g 2410 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wal 1540  wnf 1544   wceq 1642   wcel 1710  cab 2339  wnfc 2476  cvv 2859  wsbc 3046  csb 3136 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-sbc 3047  df-csb 3137 This theorem is referenced by:  csbnestg  3186  csbnest1g  3188
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