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Theorem 0elixp 4344
Description: Membership of the empty set in an infinite Cartesian product. (Contributed by Steve Rodriguez, 29-Sep-2006.)
Assertion
Ref Expression
0elixp |- (/) e. X_x e. (/) A
Proof of Theorem 0elixp
StepHypRef Expression
1 0ex 2701 . . 3 |- (/) e. V
21snid 2425 . 2 |- (/) e. {(/)}
3 ixp0x 4343 . 2 |- X_x e. (/) A = {(/)}
42, 3eleqtrr 1539 1 |- (/) e. X_x e. (/) A
Colors of variables: wff set class
Syntax hints:   e. wcel 955  (/)c0 2270  {csn 2399  X_cixp 4331
This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-11 964  ax-12 965  ax-13 966  ax-14 967  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452  ax-sep 2693  ax-nul 2700  ax-pow 2732  ax-pr 2769
This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 978  df-sb 1168  df-eu 1375  df-mo 1376  df-clab 1457  df-cleq 1462  df-clel 1465  df-ne 1579  df-ral 1641  df-v 1803  df-dif 2039  df-un 2040  df-in 2041  df-ss 2043  df-nul 2271  df-pw 2392  df-sn 2402  df-pr 2403  df-op 2406  df-br 2610  df-opab 2657  df-id 2824  df-xp 3174  df-rel 3175  df-cnv 3176  df-co 3177  df-dm 3178  df-fun 3182  df-fn 3183  df-ixp 4332
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