Metamath Proof Explorer


Theorem nbbn

Description: Move negation outside of biconditional. Compare Theorem *5.18 of WhiteheadRussell p. 124. (Contributed by NM, 27-Jun-2002) (Proof shortened by Wolf Lammen, 20-Sep-2013) (Proof shortened by Umit Teoman Dogan, 10-Jun-2026)

Ref Expression
Assertion nbbn
|- ( ( -. ph <-> ps ) <-> -. ( ph <-> ps ) )

Proof

Step Hyp Ref Expression
1 pm5.18
 |-  ( ( -. ph <-> ps ) <-> -. ( -. ph <-> -. ps ) )
2 notbi
 |-  ( ( ph <-> ps ) <-> ( -. ph <-> -. ps ) )
3 1 2 xchbinxr
 |-  ( ( -. ph <-> ps ) <-> -. ( ph <-> ps ) )