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Theorem intexg 4319
Description: The intersection of a set is a set. (Contributed by SF, 14-Jan-2015.)
Assertion
Ref Expression
intexg

Proof of Theorem intexg
StepHypRef Expression
1 dfint3 4318 . 2 ∼ ⋃1kSk k
2 ssetkex 4294 . . . . . 6 Sk
32complex 4104 . . . . 5 Sk
43cnvkex 4287 . . . 4 kSk
5 imakexg 4299 . . . 4 kSk kSk k
64, 5mpan 651 . . 3 kSk k
7 uni1exg 4292 . . 3 kSk k 1kSk k
8 complexg 4099 . . 3 1kSk k ∼ ⋃1kSk k
96, 7, 83syl 18 . 2 ∼ ⋃1kSk k
101, 9syl5eqel 2437 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wcel 1710  cvv 2859   ∼ ccompl 3205  cint 3926  ⋃1cuni1 4133  kccnvk 4175  kcimak 4179   Sk cssetk 4183
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334  ax-nin 4078  ax-xp 4079  ax-cnv 4080  ax-1c 4081  ax-sset 4082  ax-si 4083  ax-typlower 4086  ax-sn 4087
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-ral 2619  df-rex 2620  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-nul 3551  df-sn 3741  df-pr 3742  df-uni 3892  df-int 3927  df-opk 4058  df-1c 4136  df-uni1 4138  df-xpk 4185  df-cnvk 4186  df-imak 4189  df-p6 4191  df-sik 4192  df-ssetk 4193
This theorem is referenced by:  intex  4320
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