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 → 𝐴 ∈ ℝ ) | |
Assertion | cjred | ⊢ ( 𝜑 → ( ∗ ‘ 𝐴 ) = 𝐴 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | crred.1 | ⊢ ( 𝜑 → 𝐴 ∈ ℝ ) | |
2 | cjre | ⊢ ( 𝐴 ∈ ℝ → ( ∗ ‘ 𝐴 ) = 𝐴 ) | |
3 | 1 2 | syl | ⊢ ( 𝜑 → ( ∗ ‘ 𝐴 ) = 𝐴 ) |