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Theorem undif4 3607
 Description: Distribute union over difference. (Contributed by NM, 17-May-1998.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
undif4

Proof of Theorem undif4
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 pm2.621 397 . . . . . . 7
2 olc 373 . . . . . . 7
31, 2impbid1 194 . . . . . 6
43anbi2d 684 . . . . 5
5 eldif 3221 . . . . . . 7
65orbi2i 505 . . . . . 6
7 ordi 834 . . . . . 6
86, 7bitri 240 . . . . 5
9 elun 3220 . . . . . 6
109anbi1i 676 . . . . 5
114, 8, 103bitr4g 279 . . . 4
12 elun 3220 . . . 4
13 eldif 3221 . . . 4
1411, 12, 133bitr4g 279 . . 3
1514alimi 1559 . 2
16 disj1 3593 . 2
17 dfcleq 2347 . 2
1815, 16, 173imtr4i 257 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 176   wo 357   wa 358  wal 1540   wceq 1642   wcel 1710   cdif 3206   cun 3207   cin 3208  c0 3550 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-ne 2518  df-ral 2619  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-nul 3551 This theorem is referenced by: (None)
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