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Theorem undif1 3625
 Description: Absorption of difference by union. This decomposes a union into two disjoint classes (see disjdif 3622). Theorem 35 of [Suppes] p. 29. (Contributed by NM, 19-May-1998.)
Assertion
Ref Expression
undif1

Proof of Theorem undif1
StepHypRef Expression
1 undir 3504 . 2
2 invdif 3496 . . 3
32uneq1i 3414 . 2
4 uncom 3408 . . . . 5
5 undifv 3624 . . . . 5
64, 5eqtri 2373 . . . 4
76ineq2i 3454 . . 3
8 inv1 3577 . . 3
97, 8eqtri 2373 . 2
101, 3, 93eqtr3i 2381 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1642  cvv 2859   cdif 3206   cun 3207   cin 3208 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-nul 3551 This theorem is referenced by:  undif2  3626  nnsucelrlem4  4427  ssfin  4470  sfinltfin  4535
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