Metamath Proof Explorer


Theorem wl-3xornot1

Description: Flipping the first input flips the triple xor. wl-3xorrot can rotate any input to the front, so flipping any one of them does the same. (Contributed by Wolf Lammen, 1-May-2024)

Ref Expression
Assertion wl-3xornot1 ¬ hadd φ ψ χ hadd ¬ φ ψ χ

Proof

Step Hyp Ref Expression
1 wl-3xorbi hadd ¬ φ ψ χ ¬ φ ψ χ
2 nbbn ¬ φ ψ χ ¬ φ ψ χ
3 wl-3xorbi hadd φ ψ χ φ ψ χ
4 2 3 xchbinxr ¬ φ ψ χ ¬ hadd φ ψ χ
5 1 4 bitr2i ¬ hadd φ ψ χ hadd ¬ φ ψ χ