Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  sbcco3g Unicode version

Theorem sbcco3g 2960
 Description: Composition of two substitutions. (Contributed by NM, 27-Nov-2005.) (Revised by Mario Carneiro, 11-Nov-2016.)
Hypothesis
Ref Expression
sbcco3g.1
Assertion
Ref Expression
sbcco3g
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()   (,)   ()   (,)

Proof of Theorem sbcco3g
StepHypRef Expression
1 sbcnestg 2956 . 2
2 elex 2611 . . 3
3 nfcvd 2221 . . . 4
4 sbcco3g.1 . . . 4
53, 4csbiegf 2947 . . 3
6 dfsbcq 2818 . . 3
72, 5, 63syl 17 . 2
81, 7bitrd 186 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   wceq 1285   wcel 1434  cvv 2602  wsbc 2816  csb 2909 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-sbc 2817  df-csb 2910 This theorem is referenced by:  fzshftral  9201
 Copyright terms: Public domain W3C validator