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Metamath Proof Explorer

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	$⊢ φ \to A \in ℝ$
	Assertion	cjred	$⊢ φ \to \overline{A} = A$

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