Theorem 0dif 3373

Description: The difference between the empty set and a class. Part of Exercise 4.4 of [Stoll] p. 16. (Contributed by NM, 17-Aug-2004.)

Assertion

Ref	Expression
0dif	|- ( (/) \ A ) = (/)

Proof of Theorem 0dif

Step	Hyp	Ref	Expression
1		difss 3141	. 2 |- ( (/) \ A ) C_ (/)
2		ss0 3342	. 2 |- ( ( (/) \ A ) C_ (/) -> ( (/) \ A ) = (/) )
3	1, 2	ax-mp 7	1 |- ( (/) \ A ) = (/)

Syntax hints:   = wceq 1296   \ cdif 3010   C_ wss 3013   (/)c0 3302

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 582  ax-in2 583  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077

This theorem depends on definitions:  df-bi 116  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-v 2635  df-dif 3015  df-in 3019  df-ss 3026  df-nul 3303

This theorem is referenced by: (None)