Theorem 0dif 2334

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 2165	. 2 |- ((/) \ A) (_ (/)
2		ss0 2301	. 2 |- (((/) \ A) (_ (/) -> ((/) \ A) = (/))
3	1, 2	ax-mp 7	1 |- ((/) \ A) = (/)

Syntax hints:   = wceq 955   \ cdif 2042   (_ wss 2045  (/)c0 2278

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 961  ax-gen 962  ax-8 963  ax-10 965  ax-12 967  ax-17 970  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-10o 1139  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 980  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1810  df-dif 2047  df-in 2049  df-ss 2051  df-nul 2279

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