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

Theorem iinxsng 3758
 Description: A singleton index picks out an instance of an indexed intersection's argument. (Contributed by NM, 15-Jan-2012.) (Proof shortened by Mario Carneiro, 17-Nov-2016.)
Hypothesis
Ref Expression
iinxsng.1
Assertion
Ref Expression
iinxsng
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem iinxsng
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-iin 3688 . 2
2 iinxsng.1 . . . . 5
32eleq2d 2123 . . . 4
43ralsng 3439 . . 3
54abbi1dv 2173 . 2
61, 5syl5eq 2100 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1259   wcel 1409  cab 2042  wral 2323  csn 3403  ciin 3686 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-ral 2328  df-v 2576  df-sbc 2788  df-sn 3409  df-iin 3688 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator