Theorem incomOLD

Description: Obsolete version of incom as of 12-Dec-2023. Commutative law for intersection of classes. Exercise 7 of TakeutiZaring p. 17. (Contributed by NM, 21-Jun-1993) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Assertion	incomOLD	|- ( A i^i B ) = ( B i^i A )

Proof

Step	Hyp	Ref	Expression
1		ancom	|- ( ( x e. A /\ x e. B ) <-> ( x e. B /\ x e. A ) )
2		elin	|- ( x e. ( A i^i B ) <-> ( x e. A /\ x e. B ) )
3		elin	|- ( x e. ( B i^i A ) <-> ( x e. B /\ x e. A ) )
4	1 2 3	3bitr4i	|- ( x e. ( A i^i B ) <-> x e. ( B i^i A ) )
5	4	eqriv	|- ( A i^i B ) = ( B i^i A )