Theorem cjred

Description: A real number equals its complex conjugate. 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	cjred	$$⊢\phi \to \bar{A}=A$$

Proof

Step	Hyp	Ref	Expression
1		crred.1	$$⊢\phi \to A\in ℝ$$
2		cjre	$$⊢A\in ℝ\to \bar{A}=A$$
3	1 2	syl	$$⊢\phi \to \bar{A}=A$$