Metamath Proof Explorer


Theorem nancom

Description: Alternative denial is commutative. Remark: alternative denial is not associative, see nanass . (Contributed by Mario Carneiro, 9-May-2015) (Proof shortened by Wolf Lammen, 26-Jun-2020)

Ref Expression
Assertion nancom φ ψ ψ φ

Proof

Step Hyp Ref Expression
1 con2b φ ¬ ψ ψ ¬ φ
2 dfnan2 φ ψ φ ¬ ψ
3 dfnan2 ψ φ ψ ¬ φ
4 1 2 3 3bitr4i φ ψ ψ φ