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Theorem dfun3 3717
 Description: Union defined in terms of intersection (De Morgan's law). Definition of union in [Mendelson] p. 231. (Contributed by NM, 8-Jan-2002.)
Assertion
Ref Expression
dfun3

Proof of Theorem dfun3
StepHypRef Expression
1 dfun2 3714 . 2
2 dfin2 3715 . . . 4
3 ddif 3603 . . . . 5
43difeq2i 3586 . . . 4
52, 4eqtr2i 2459 . . 3
65difeq2i 3586 . 2
71, 6eqtri 2458 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1437  cvv 3087   cdif 3439   cun 3440   cin 3441 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ral 2787  df-rab 2791  df-v 3089  df-dif 3445  df-un 3447  df-in 3449 This theorem is referenced by:  difundi  3731  unvdif  3875
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