Metamath Proof Explorer

Theorem annim

Description: Express a conjunction in terms of a negated implication. (Contributed by NM, 2-Aug-1994)

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

Proof

Step Hyp Ref Expression
1 iman 
 |-  ( ( ph -> ps ) <-> -. ( ph /\ -. ps ) )
2 1 con2bii 
 |-  ( ( ph /\ -. ps ) <-> -. ( ph -> ps ) )