Theorem negcon2

Description: Negative contraposition law. (Contributed by NM, 14-Nov-2004)

	Ref	Expression
Assertion	negcon2	|- ( ( A e. CC /\ B e. CC ) -> ( A = -u B <-> B = -u A ) )

Proof

Step	Hyp	Ref	Expression
1		eqcom	|- ( A = -u B <-> -u B = A )
2		negcon1	|- ( ( A e. CC /\ B e. CC ) -> ( -u A = B <-> -u B = A ) )
3	1 2	bitr4id	|- ( ( A e. CC /\ B e. CC ) -> ( A = -u B <-> -u A = B ) )
4		eqcom	|- ( -u A = B <-> B = -u A )
5	3 4	bitrdi	|- ( ( A e. CC /\ B e. CC ) -> ( A = -u B <-> B = -u A ) )