Theorem rele2

Description: The ordering relation of the field of reals. (Contributed by Thierry Arnoux, 21-Jan-2018)

	Ref	Expression
Assertion	rele2	⊢ ≤ = ( le ‘ ℝfld )

Proof

Step	Hyp	Ref	Expression
1		reex	⊢ ℝ ∈ V
2		df-refld	⊢ ℝfld = ( ℂfld ↾s ℝ )
3		cnfldle	⊢ ≤ = ( le ‘ ℂfld )
4	2 3	ressle	⊢ ( ℝ ∈ V → ≤ = ( le ‘ ℝfld ) )
5	1 4	ax-mp	⊢ ≤ = ( le ‘ ℝfld )