Theorem sdomn2lp

Description: Strict dominance has no 2-cycle loops. (Contributed by NM, 6-May-2008)

	Ref	Expression
Assertion	sdomn2lp	$$⊢\neg \left(A\prec B\wedge B\prec A\right)$$

Proof

Step	Hyp	Ref	Expression
1		sdomirr	$$⊢\neg A\prec A$$
2		sdomtr	$$⊢\left(A\prec B\wedge B\prec A\right)\to A\prec A$$
3	1 2	mto	$$⊢\neg \left(A\prec B\wedge B\prec A\right)$$