Metamath Proof Explorer

Theorem imnani

Description: Infer an implication from a negated conjunction. (Contributed by Mario Carneiro, 28-Sep-2015)

Ref Expression
Hypothesis imnani.1 
|- -. ( ph /\ ps )
Assertion imnani 
|- ( ph -> -. ps )

Proof

Step Hyp Ref Expression
1 imnani.1 
 |-  -. ( ph /\ ps )
2 imnan 
 |-  ( ( ph -> -. ps ) <-> -. ( ph /\ ps ) )
3 1 2 mpbir 
 |-  ( ph -> -. ps )