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Theorem iundifdif 24013
 Description: The intersection of a set is the complement of the union of the complements. TODO shorten using iundifdifd 24012 (Contributed by Thierry Arnoux, 4-Sep-2016.)
Hypotheses
Ref Expression
iundifdif.o
iundifdif.2
Assertion
Ref Expression
iundifdif
Distinct variable groups:   ,   ,

Proof of Theorem iundifdif
StepHypRef Expression
1 iundif2 4158 . . . 4
2 intiin 4145 . . . . 5
32difeq2i 3462 . . . 4
41, 3eqtr4i 2459 . . 3
54difeq2i 3462 . 2
6 iundifdif.2 . . . . 5
76jctl 526 . . . 4
8 intssuni2 4075 . . . 4
9 unipw 4414 . . . . . 6
109sseq2i 3373 . . . . 5
1110biimpi 187 . . . 4
127, 8, 113syl 19 . . 3
13 dfss4 3575 . . 3
1412, 13sylib 189 . 2
155, 14syl5req 2481 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725   wne 2599  cvv 2956   cdif 3317   wss 3320  c0 3628  cpw 3799  cuni 4015  cint 4050  ciun 4093  ciin 4094 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-pw 3801  df-sn 3820  df-pr 3821  df-uni 4016  df-int 4051  df-iun 4095  df-iin 4096
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