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Theorem symdifeq2 3249
 Description: Equality law for intersection. (Contributed by SF, 11-Jan-2015.)
Assertion
Ref Expression
symdifeq2

Proof of Theorem symdifeq2
StepHypRef Expression
1 difeq2 3247 . . . 4
21compleqd 3245 . . 3
3 difeq1 3246 . . . 4
43compleqd 3245 . . 3
52, 4nineq12d 3242 . 2 &ncap ∼ &ncap ∼
6 df-symdif 3216 . . 3
7 df-un 3214 . . 3 &ncap ∼
86, 7eqtri 2373 . 2 &ncap ∼
9 df-symdif 3216 . . 3
10 df-un 3214 . . 3 &ncap ∼
119, 10eqtri 2373 . 2 &ncap ∼
125, 8, 113eqtr4g 2410 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1642   &ncap cnin 3204   ∼ ccompl 3205   cdif 3206   cun 3207   csymdif 3209 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  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-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-symdif 3216 This theorem is referenced by:  symdifeq12  3250  symdifeq2i  3252  symdifeq2d  3255
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