Metamath Proof Explorer

Theorem norcom

Description: The connector -\/ is commutative. (Contributed by Remi, 25-Oct-2023) (Proof shortened by Wolf Lammen, 23-Apr-2024)

Ref Expression
Assertion norcom 
|- ( ( ph -\/ ps ) <-> ( ps -\/ ph ) )

Proof

Step Hyp Ref Expression
1 df-nor 
 |-  ( ( ph -\/ ps ) <-> -. ( ph \/ ps ) )
2 orcom 
 |-  ( ( ph \/ ps ) <-> ( ps \/ ph ) )
3 1 2 xchbinx 
 |-  ( ( ph -\/ ps ) <-> -. ( ps \/ ph ) )
4 df-nor 
 |-  ( ( ps -\/ ph ) <-> -. ( ps \/ ph ) )
5 3 4 bitr4i 
 |-  ( ( ph -\/ ps ) <-> ( ps -\/ ph ) )