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Theorem dfss4 3489
 Description: Subclass defined in terms of class difference. See comments under dfun2 3490. (Contributed by NM, 22-Mar-1998.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
dfss4

Proof of Theorem dfss4
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sseqin2 3474 . 2
2 eldif 3221 . . . . . . 7
32notbii 287 . . . . . 6
43anbi2i 675 . . . . 5
5 elin 3219 . . . . . 6
6 abai 770 . . . . . 6
7 iman 413 . . . . . . 7
87anbi2i 675 . . . . . 6
95, 6, 83bitri 262 . . . . 5
104, 9bitr4i 243 . . . 4
1110difeqri 3387 . . 3
1211eqeq1i 2360 . 2
131, 12bitr4i 243 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 176   wa 358   wceq 1642   wcel 1710   cdif 3206   cin 3208   wss 3257 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-dif 3215  df-ss 3259 This theorem is referenced by:  dfin4  3495
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