Metamath Proof Explorer


Theorem difid

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) (Revised by David Abernethy, 17-Jun-2012)

Ref Expression
Assertion difid AA=

Proof

Step Hyp Ref Expression
1 dfdif2 AA=xA|¬xA
2 dfnul3 =xA|¬xA
3 1 2 eqtr4i AA=