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Theorem ixpin 7514
 Description: The intersection of two infinite Cartesian products. (Contributed by Mario Carneiro, 3-Feb-2015.)
Assertion
Ref Expression
ixpin
Distinct variable group:   ,

Proof of Theorem ixpin
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 anandi 828 . . . 4
2 elin 3686 . . . . . . 7
32ralbii 2888 . . . . . 6
4 r19.26 2984 . . . . . 6
53, 4bitri 249 . . . . 5
65anbi2i 694 . . . 4
7 vex 3112 . . . . . 6
87elixp 7496 . . . . 5
97elixp 7496 . . . . 5
108, 9anbi12i 697 . . . 4
111, 6, 103bitr4i 277 . . 3
127elixp 7496 . . 3
13 elin 3686 . . 3
1411, 12, 133bitr4i 277 . 2
1514eqriv 2453 1
 Colors of variables: wff setvar class Syntax hints:  /\wa 369  =wceq 1395  e.wcel 1818  A.wral 2807  i^icin 3474  Fnwfn 5588  cfv 5593  X_`cixp 7489 This theorem is referenced by:  ptbasin  20078  ptclsg  20116  ptrest  30048 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-iota 5556  df-fun 5595  df-fn 5596  df-fv 5601  df-ixp 7490
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