Theorem ex-gt

Description: Simple example of > , in this case, 0 is not greater than 0. This is useful as an example, and helps us gain confidence that we've correctly defined the symbol. (Contributed by David A. Wheeler, 1-Jan-2017) (New usage is discouraged.)

	Ref	Expression
Assertion	ex-gt	⊢ ¬ 0 > 0

Proof

Step	Hyp	Ref	Expression
1		0re	⊢ 0 ∈ ℝ
2	1	ltnri	⊢ ¬ 0 < 0
3		c0ex	⊢ 0 ∈ V
4	3 3	gt-lth	⊢ ( 0 > 0 ↔ 0 < 0 )
5	2 4	mtbir	⊢ ¬ 0 > 0