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Theorem ddif 3443
 Description: Double complement under universal class. Exercise 4.10(s) of [Mendelson] p. 231. (Contributed by NM, 8-Jan-2002.)
Assertion
Ref Expression
ddif

Proof of Theorem ddif
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2923 . . . . 5
2 eldif 3294 . . . . 5
31, 2mpbiran 885 . . . 4
43con2bii 323 . . 3
51biantrur 493 . . 3
64, 5bitr2i 242 . 2
76difeqri 3431 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 359   wceq 1649   wcel 1721  cvv 2920   cdif 3281 This theorem is referenced by:  dfun3  3543  dfin3  3544  invdif  3546  ssindif0  3645  difdifdir  3679 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2395  df-cleq 2401  df-clel 2404  df-nfc 2533  df-v 2922  df-dif 3287
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