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Theorem dfun2 3568
 Description: An alternate definition of the union of two classes in terms of class difference, requiring no dummy variables. Along with dfin2 3569 and dfss4 3567 it shows we can express union, intersection, and subset directly in terms of the single "primitive" operation (class difference). (Contributed by NM, 10-Jun-2004.)
Assertion
Ref Expression
dfun2

Proof of Theorem dfun2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2951 . . . . . . 7
2 eldif 3322 . . . . . . 7
31, 2mpbiran 885 . . . . . 6
43anbi1i 677 . . . . 5
5 eldif 3322 . . . . 5
6 ioran 477 . . . . 5
74, 5, 63bitr4i 269 . . . 4
87con2bii 323 . . 3
9 eldif 3322 . . . 4
101, 9mpbiran 885 . . 3
118, 10bitr4i 244 . 2
1211uneqri 3481 1
 Colors of variables: wff set class Syntax hints:   wn 3   wo 358   wa 359   wceq 1652   wcel 1725  cvv 2948   cdif 3309   cun 3310 This theorem is referenced by:  dfun3  3571  dfin3  3572 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-dif 3315  df-un 3317
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