Metamath Proof Explorer

Theorem pm4.54

Description: Theorem *4.54 of WhiteheadRussell p. 120. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 5-Nov-2012)

Ref Expression
Assertion pm4.54 
|- ( ( -. ph /\ ps ) <-> -. ( ph \/ -. ps ) )

Proof

Step Hyp Ref Expression
1 df-an 
 |-  ( ( -. ph /\ ps ) <-> -. ( -. ph -> -. ps ) )
2 pm4.66 
 |-  ( ( -. ph -> -. ps ) <-> ( ph \/ -. ps ) )
3 1 2 xchbinx 
 |-  ( ( -. ph /\ ps ) <-> -. ( ph \/ -. ps ) )