Theorem epsoon

Description: The ordinals are strictly and completely (linearly) ordered. Theorem 1.9 of Schloeder p. 1. Based on epweon and weso . (Contributed by RP, 15-Jan-2025)

	Ref	Expression
Assertion	epsoon	$$⊢\mathrm{E}\mathrm{Or}\mathrm{On}$$

Proof

Step	Hyp	Ref	Expression
1		epweon	$$⊢\mathrm{E}\mathrm{We}\mathrm{On}$$
2		weso	$$⊢\mathrm{E}\mathrm{We}\mathrm{On}\to \mathrm{E}\mathrm{Or}\mathrm{On}$$
3	1 2	ax-mp	$$⊢\mathrm{E}\mathrm{Or}\mathrm{On}$$