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

Theorem csbiotag 4923
 Description: Class substitution within a description binder. (Contributed by Scott Fenton, 6-Oct-2017.)
Assertion
Ref Expression
csbiotag
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   ()   (,)

Proof of Theorem csbiotag
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbeq1 2883 . . 3
2 dfsbcq2 2790 . . . 4
32iotabidv 4916 . . 3
41, 3eqeq12d 2070 . 2
5 vex 2577 . . 3
6 nfs1v 1831 . . . 4
76nfiotaxy 4899 . . 3
8 sbequ12 1670 . . . 4
98iotabidv 4916 . . 3
105, 7, 9csbief 2919 . 2
114, 10vtoclg 2630 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1259   wcel 1409  wsb 1661  wsbc 2787  csb 2880  cio 4893 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-rex 2329  df-v 2576  df-sbc 2788  df-csb 2881  df-sn 3409  df-uni 3609  df-iota 4895 This theorem is referenced by:  csbfv12g  5237
 Copyright terms: Public domain W3C validator