Metamath Proof Explorer


Theorem cjcji

Description: The conjugate of the conjugate is the original complex number. Proposition 10-3.4(e) of Gleason p. 133. (Contributed by NM, 11-May-1999)

Ref Expression
Hypothesis recl.1
|- A e. CC
Assertion cjcji
|- ( * ` ( * ` A ) ) = A

Proof

Step Hyp Ref Expression
1 recl.1
 |-  A e. CC
2 cjcj
 |-  ( A e. CC -> ( * ` ( * ` A ) ) = A )
3 1 2 ax-mp
 |-  ( * ` ( * ` A ) ) = A