df-le - Intuitionistic Logic Explorer

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Definition df-le 8067

Description: Define 'less than or equal to' on the extended real subset of complex numbers. (Contributed by NM, 13-Oct-2005.)

**Assertion**
Ref	Expression
df-le	⊢ ≤ = ((ℝ^* × ℝ^*) ∖ ^◡ < )

**Detailed syntax breakdown of Definition df-le**
Step	Hyp	Ref	Expression
1		cle 8062	. 2 class ≤
2		cxr 8060	. . . 4 class ℝ^*
3	2, 2	cxp 4661	. . 3 class (ℝ^* × ℝ^*)
4		clt 8061	. . . 4 class <
5	4	ccnv 4662	. . 3 class ^◡ <
6	3, 5	cdif 3154	. 2 class ((ℝ^* × ℝ^*) ∖ ^◡ < )
7	1, 6	wceq 1364	1 wff ≤ = ((ℝ^* × ℝ^*) ∖ ^◡ < )

Colors of variables: wff set class

This definition is referenced by: lerelxr 8089 xrlenlt 8091