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

Theorem iinxprg 3731
 Description: Indexed intersection with an unordered pair index. (Contributed by NM, 25-Jan-2012.)
Hypotheses
Ref Expression
iinxprg.1
iinxprg.2
Assertion
Ref Expression
iinxprg
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem iinxprg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 iinxprg.1 . . . . 5
21eleq2d 2107 . . . 4
3 iinxprg.2 . . . . 5
43eleq2d 2107 . . . 4
52, 4ralprg 3421 . . 3
65abbidv 2155 . 2
7 df-iin 3660 . 2
8 df-in 2924 . 2
96, 7, 83eqtr4g 2097 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wceq 1243   wcel 1393  cab 2026  wral 2306   cin 2916  cpr 3376  ciin 3658 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-ral 2311  df-v 2559  df-sbc 2765  df-un 2922  df-in 2924  df-sn 3381  df-pr 3382  df-iin 3660 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator