Theorem cvnref

Description: The covers relation is not reflexive. (Contributed by NM, 26-Jun-2004) (New usage is discouraged.)

	Ref	Expression
Assertion	cvnref	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}\to \neg A{⋖}_{\mathscr{H}}A$$

Proof

Step	Hyp	Ref	Expression
1		cvnsym	$$⊢\left(A\in {\mathbf{C}}_{\mathscr{H}}\wedge A\in {\mathbf{C}}_{\mathscr{H}}\right)\to \left(A{⋖}_{\mathscr{H}}A\to \neg A{⋖}_{\mathscr{H}}A\right)$$
2	1	anidms	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}\to \left(A{⋖}_{\mathscr{H}}A\to \neg A{⋖}_{\mathscr{H}}A\right)$$
3	2	pm2.01d	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}\to \neg A{⋖}_{\mathscr{H}}A$$