Metamath Proof Explorer


Theorem fixcnv

Description: The fixpoints of a class are the same as those of its converse. (Contributed by Scott Fenton, 16-Apr-2012)

Ref Expression
Assertion fixcnv 𝖥𝗂𝗑 A = 𝖥𝗂𝗑 A -1

Proof

Step Hyp Ref Expression
1 vex x V
2 1 1 brcnv x A -1 x x A x
3 1 elfix x 𝖥𝗂𝗑 A -1 x A -1 x
4 1 elfix x 𝖥𝗂𝗑 A x A x
5 2 3 4 3bitr4ri x 𝖥𝗂𝗑 A x 𝖥𝗂𝗑 A -1
6 5 eqriv 𝖥𝗂𝗑 A = 𝖥𝗂𝗑 A -1