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Theorem difid 3458
 Description: The difference between a class and itself is the empty set. Proposition 5.15 of [TakeutiZaring] p. 20. Also Theorem 32 of [Suppes] p. 28. (Contributed by NM, 22-Apr-2004.)
Assertion
Ref Expression
difid

Proof of Theorem difid
StepHypRef Expression
1 ssid 3144 . 2
2 ssdif0im 3454 . 2
31, 2ax-mp 5 1
 Colors of variables: wff set class Syntax hints:   wceq 1332   cdif 3095   wss 3098  c0 3390 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-v 2711  df-dif 3100  df-in 3104  df-ss 3111  df-nul 3391 This theorem is referenced by:  dif0  3460  difun2  3469  diftpsn3  3693  2oconcl  6376  ismkvnex  7077  topcld  12448
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