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Theorem ixpin 7079
 Description: The intersection of two infinite Cartesian products. (Contributed by Mario Carneiro, 3-Feb-2015.)
Assertion
Ref Expression
ixpin
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem ixpin
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 anandi 802 . . . 4
2 elin 3522 . . . . . . 7
32ralbii 2721 . . . . . 6
4 r19.26 2830 . . . . . 6
53, 4bitri 241 . . . . 5
65anbi2i 676 . . . 4
7 vex 2951 . . . . . 6
87elixp 7061 . . . . 5
97elixp 7061 . . . . 5
108, 9anbi12i 679 . . . 4
111, 6, 103bitr4i 269 . . 3
127elixp 7061 . . 3
13 elin 3522 . . 3
1411, 12, 133bitr4i 269 . 2
1514eqriv 2432 1
 Colors of variables: wff set class Syntax hints:   wa 359   wceq 1652   wcel 1725  wral 2697   cin 3311   wfn 5441  cfv 5446  cixp 7055 This theorem is referenced by:  ptbasin  17601  ptclsg  17639 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-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-iota 5410  df-fun 5448  df-fn 5449  df-fv 5454  df-ixp 7056
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