Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  cbvopab1s Unicode version

Theorem cbvopab1s 3832
 Description: Change first bound variable in an ordered-pair class abstraction, using explicit substitution. (Contributed by NM, 31-Jul-2003.)
Assertion
Ref Expression
cbvopab1s
Distinct variable groups:   ,,   ,
Allowed substitution hints:   (,)

Proof of Theorem cbvopab1s
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1421 . . . 4
2 nfv 1421 . . . . . 6
3 nfs1v 1815 . . . . . 6
42, 3nfan 1457 . . . . 5
54nfex 1528 . . . 4
6 opeq1 3549 . . . . . . 7
76eqeq2d 2051 . . . . . 6
8 sbequ12 1654 . . . . . 6
97, 8anbi12d 442 . . . . 5
109exbidv 1706 . . . 4
111, 5, 10cbvex 1639 . . 3
1211abbii 2153 . 2
13 df-opab 3819 . 2
14 df-opab 3819 . 2
1512, 13, 143eqtr4i 2070 1
 Colors of variables: wff set class Syntax hints:   wa 97   wceq 1243  wex 1381  wsb 1645  cab 2026  cop 3378  copab 3817 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-opab 3819 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator