Metamath Proof Explorer

Theorem biortn

Description: A wff is equivalent to its negated disjunction with falsehood. (Contributed by NM, 9-Jul-2012)

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

Proof

Step Hyp Ref Expression
1 notnot 
 |-  ( ph -> -. -. ph )
2 biorf 
 |-  ( -. -. ph -> ( ps <-> ( -. ph \/ ps ) ) )
3 1 2 syl 
 |-  ( ph -> ( ps <-> ( -. ph \/ ps ) ) )