Theorem ltsirr

Description: Surreal less-than is irreflexive. (Contributed by Scott Fenton, 16-Jun-2011)

	Ref	Expression
Assertion	ltsirr	⊢ ( 𝐴 ∈ No → ¬ 𝐴 <s 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		ltsso	⊢ <s Or No
2		sonr	⊢ ( ( <s Or No ∧ 𝐴 ∈ No ) → ¬ 𝐴 <s 𝐴 )
3	1 2	mpan	⊢ ( 𝐴 ∈ No → ¬ 𝐴 <s 𝐴 )