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Theorem iinxprg 4350
 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 2534 . . . 4
3 iinxprg.2 . . . . 5
43eleq2d 2534 . . . 4
52, 4ralprg 4012 . . 3
65abbidv 2589 . 2
7 df-iin 4272 . 2
8 df-in 3397 . 2
96, 7, 83eqtr4g 2530 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 376   wceq 1452   wcel 1904  cab 2457  wral 2756   cin 3389  cpr 3961  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-or 377  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-nfc 2601  df-ral 2761  df-v 3033  df-sbc 3256  df-un 3395  df-in 3397  df-sn 3960  df-pr 3962  df-iin 4272 This theorem is referenced by:  pmapmeet  33409  diameetN  34695  dihmeetlem2N  34938  dihmeetcN  34941  dihmeet  34982
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