Theorem 0dif 2336

Description: The difference between the empty set and a class. Part of Exercise 4.4 of [Stoll] p. 16.

Assertion

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

Proof of Theorem 0dif

Step	Hyp	Ref	Expression
1		difss 2167	. 2 |- ((/) \ A) (_ (/)
2		ss0 2303	. 2 |- (((/) \ A) (_ (/) -> ((/) \ A) = (/))
3	1, 2	ax-mp 7	1 |- ((/) \ A) = (/)

Syntax hints:   = wceq 956   \ cdif 2044   (_ wss 2047  (/)c0 2280

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-dif 2049  df-in 2051  df-ss 2053  df-nul 2281

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