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Theorem dfin3 3736
 Description: Intersection defined in terms of union (De Morgan's law). Similar to Exercise 4.10(n) of [Mendelson] p. 231. (Contributed by NM, 8-Jan-2002.)
Assertion
Ref Expression
dfin3

Proof of Theorem dfin3
StepHypRef Expression
1 ddif 3635 . 2
2 dfun2 3732 . . . 4
3 ddif 3635 . . . . . 6
43difeq1i 3617 . . . . 5
54difeq2i 3618 . . . 4
62, 5eqtri 2486 . . 3
76difeq2i 3618 . 2
8 dfin2 3733 . 2
91, 7, 83eqtr4ri 2497 1
 Colors of variables: wff setvar class Syntax hints:  =wceq 1395   cvv 3109  \cdif 3472  u.cun 3473  i^icin 3474 This theorem is referenced by:  difindi  3751 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-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-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482
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