Theorem refldcj

Description: The conjugation operation of the field of real numbers. (Contributed by Thierry Arnoux, 30-Jun-2019)

	Ref	Expression
Assertion	refldcj	⊢ ∗ = ( *𝑟 ‘ ℝfld )

Proof

Step	Hyp	Ref	Expression
1		reex	⊢ ℝ ∈ V
2		df-refld	⊢ ℝfld = ( ℂfld ↾s ℝ )
3		cnfldcj	⊢ ∗ = ( *𝑟 ‘ ℂfld )
4	2 3	ressstarv	⊢ ( ℝ ∈ V → ∗ = ( *𝑟 ‘ ℝfld ) )
5	1 4	ax-mp	⊢ ∗ = ( *𝑟 ‘ ℝfld )