**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 | $${\u22a2}{\phi}\to {A}\in \mathbb{R}$$ | |

Assertion | cjred | $${\u22a2}{\phi}\to \stackrel{\u203e}{{A}}={A}$$ |

Step | Hyp | Ref | Expression |
---|---|---|---|

1 | crred.1 | $${\u22a2}{\phi}\to {A}\in \mathbb{R}$$ | |

2 | cjre | $${\u22a2}{A}\in \mathbb{R}\to \stackrel{\u203e}{{A}}={A}$$ | |

3 | 1 2 | syl | $${\u22a2}{\phi}\to \stackrel{\u203e}{{A}}={A}$$ |