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Theorem difidALT 3429
 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. (Alternate proof of difid 3428 suggested by David Abernethy, 17-Jun-2012.) (Contributed by NM, 17-Jun-2012.) (Proof modification is discouraged.)
Assertion
Ref Expression
difidALT

Proof of Theorem difidALT
StepHypRef Expression
1 dfdif2 3087 . 2
2 dfnul3 3365 . 2
31, 2eqtr4i 2276 1
 Colors of variables: wff set class Syntax hints:   wn 5   wceq 1619   wcel 1621  crab 2512   cdif 3075  c0 3362 This theorem is referenced by:  fin1a2lem13  7922 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-rab 2516  df-v 2729  df-dif 3081  df-nul 3363
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