Theorem disj2 3124

Description: Two ways of saying that two classes are disjoint.

Assertion

Ref	Expression
disj2	|- ((A i^i B) = (/) <-> A C_ (_V \ B))

Proof of Theorem disj2

Step	Hyp	Ref	Expression
1		ssv 2864	. 2 |- A C_ _V
2		reldisj 3121	. 2 |- (A C_ _V -> ((A i^i B) = (/) <-> A C_ (_V \ B)))
3	1, 2	ax-mp 7	1 |- ((A i^i B) = (/) <-> A C_ (_V \ B))

Syntax hints:   <-> wb 219   = wceq 1586  _Vcvv 2538   \ cdif 2824   i^i cin 2826   C_ wss 2827  (/)c0 3082

This theorem is referenced by:  ssindif0 3130  intirr 4425

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1592  ax-gen 1593  ax-8 1594  ax-9 1595  ax-10 1596  ax-11 1597  ax-12 1598  ax-17 1605  ax-4 1608  ax-5o 1610  ax-6o 1613  ax-9o 1763  ax-10o 1781  ax-16 1854  ax-11o 1864  ax-ext 2123

This theorem depends on definitions:  df-bi 220  df-or 338  df-an 339  df-ex 1616  df-sb 1816  df-clab 2129  df-cleq 2134  df-clel 2137  df-ral 2359  df-v 2540  df-dif 2830  df-in 2834  df-ss 2836  df-nul 3083

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