Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  dfin3 Unicode version

Theorem dfin3 3315
 Description: Intersection defined in terms of union (DeMorgan'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 3222 . 2
2 dfun2 3311 . . . 4
3 ddif 3222 . . . . . 6
43difeq1i 3207 . . . . 5
54difeq2i 3208 . . . 4
62, 5eqtri 2273 . . 3
76difeq2i 3208 . 2
8 dfin2 3312 . 2
91, 7, 83eqtr4ri 2284 1
 Colors of variables: wff set class Syntax hints:   wceq 1619  cvv 2727   cdif 3075   cun 3076   cin 3077 This theorem is referenced by:  difindi  3330 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ral 2513  df-rab 2516  df-v 2729  df-dif 3081  df-un 3083  df-in 3085
 Copyright terms: Public domain W3C validator