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Theorem csbnest1g 3296
 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 3276 . . . 4
21ax-gen 1555 . . 3
3 csbnestgf 3292 . . 3
42, 3mpan2 653 . 2
5 csbco 3253 . . 3
65csbeq2i 3270 . 2
7 csbco 3253 . 2
84, 6, 73eqtr3g 2491 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1549   wceq 1652   wcel 1725  wnfc 2559  csb 3244 This theorem is referenced by:  csbidmg  3297 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2951  df-sbc 3155  df-csb 3245
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