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Theorem iinxsng 4042
 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 3972 . 2
2 iinxsng.1 . . . . 5
32eleq2d 2420 . . . 4
43ralsng 3765 . . 3
54abbi1dv 2469 . 2
61, 5syl5eq 2397 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1642   wcel 1710  cab 2339  wral 2614  csn 3737  ciin 3970 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-v 2861  df-sbc 3047  df-sn 3741  df-iin 3972 This theorem is referenced by: (None)
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