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Theorem iinxsng 4349
 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 4272 . 2
2 iinxsng.1 . . . . 5
32eleq2d 2534 . . . 4
43ralsng 3997 . . 3
54abbi1dv 2591 . 2
61, 5syl5eq 2517 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1452   wcel 1904  cab 2457  wral 2756  csn 3959  ciin 4270 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-ral 2761  df-v 3033  df-sbc 3256  df-sn 3960  df-iin 4272 This theorem is referenced by:  polatN  33567
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