Theorem rered

Description: A real number equals its real part. One direction of Proposition 10-3.4(f) of Gleason p. 133. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypothesis	crred.1	$$⊢\phi \to A\in ℝ$$
Assertion	rered	$$⊢\phi \to \Re \left(A\right)=A$$

Proof

Step	Hyp	Ref	Expression
1		crred.1	$$⊢\phi \to A\in ℝ$$
2		rere	$$⊢A\in ℝ\to \Re \left(A\right)=A$$
3	1 2	syl	$$⊢\phi \to \Re \left(A\right)=A$$