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Theorem iinxsng 4167
 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 4096 . 2
2 iinxsng.1 . . . . 5
32eleq2d 2503 . . . 4
43ralsng 3846 . . 3
54abbi1dv 2552 . 2
61, 5syl5eq 2480 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  cab 2422  wral 2705  csn 3814  ciin 4094 This theorem is referenced by:  polatN  30728 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-v 2958  df-sbc 3162  df-sn 3820  df-iin 4096
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