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Theorem iinxprg 4160
 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 2502 . . . 4
3 iinxprg.2 . . . . 5
43eleq2d 2502 . . . 4
52, 4ralprg 3849 . . 3
65abbidv 2549 . 2
7 df-iin 4088 . 2
8 df-in 3319 . 2
96, 7, 83eqtr4g 2492 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725  cab 2421  wral 2697   cin 3311  cpr 3807  ciin 4086 This theorem is referenced by:  pmapmeet  30507  diameetN  31791  dihmeetlem2N  32034  dihmeetcN  32037  dihmeet  32078 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 2416 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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-v 2950  df-sbc 3154  df-un 3317  df-in 3319  df-sn 3812  df-pr 3813  df-iin 4088
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