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Theorem sbcnestg 2927
 Description: Nest the composition of two substitutions. (Contributed by NM, 27-Nov-2005.) (Proof shortened by Mario Carneiro, 11-Nov-2016.)
Assertion
Ref Expression
sbcnestg
Distinct variable group:   ,
Allowed substitution hints:   ()   (,)   (,)   (,)

Proof of Theorem sbcnestg
StepHypRef Expression
1 nfv 1437 . . 3
21ax-gen 1354 . 2
3 sbcnestgf 2925 . 2
42, 3mpan2 409 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 102  wal 1257  wnf 1365   wcel 1409  wsbc 2787  csb 2880 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-sbc 2788  df-csb 2881 This theorem is referenced by:  sbcco3g  2931
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