MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  dfoprab2 Unicode version

Theorem dfoprab2 6343
Description: Class abstraction for operations in terms of class abstraction of ordered pairs. (Contributed by NM, 12-Mar-1995.)
Assertion
Ref Expression
dfoprab2
Distinct variable groups:   , ,   , ,   ,

Proof of Theorem dfoprab2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 excom 1849 . . . 4
2 exrot4 1853 . . . . 5
3 opeq1 4217 . . . . . . . . . . . 12
43eqeq2d 2471 . . . . . . . . . . 11
54pm5.32ri 638 . . . . . . . . . 10
65anbi1i 695 . . . . . . . . 9
7 anass 649 . . . . . . . . 9
8 an32 798 . . . . . . . . 9
96, 7, 83bitr3i 275 . . . . . . . 8
109exbii 1667 . . . . . . 7
11 opex 4716 . . . . . . . . 9
1211isseti 3115 . . . . . . . 8
13 19.42v 1775 . . . . . . . 8
1412, 13mpbiran2 919 . . . . . . 7
1510, 14bitri 249 . . . . . 6
16153exbii 1669 . . . . 5
172, 16bitri 249 . . . 4
18 19.42vv 1777 . . . . 5
19182exbii 1668 . . . 4
201, 17, 193bitr3i 275 . . 3
2120abbii 2591 . 2
22 df-oprab 6300 . 2
23 df-opab 4511 . 2
2421, 22, 233eqtr4i 2496 1
Colors of variables: wff setvar class
Syntax hints:  /\wa 369  =wceq 1395  E.wex 1612  {cab 2442  <.cop 4035  {copab 4509  {coprab 6297
This theorem is referenced by:  reloprab  6344  oprabv  6345  cbvoprab1  6369  cbvoprab12  6371  cbvoprab3  6373  dmoprab  6383  rnoprab  6385  ssoprab2i  6391  mpt2mptx  6393  resoprab  6398  funoprabg  6401  elrnmpt2res  6416  ov6g  6440  dfoprab3s  6855  xpcomco  7627  omxpenlem  7638  nvss  25486  mpt2mptxf  27518  mpt2mptx2  32924
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-opab 4511  df-oprab 6300
  Copyright terms: Public domain W3C validator