Metamath Proof Explorer


Theorem jcnd

Description: Deduction joining the consequents of two premises. (Contributed by Glauco Siliprandi, 11-Dec-2019) (Proof shortened by Wolf Lammen, 10-Apr-2024)

Ref Expression
Hypotheses jcnd.1
|- ( ph -> ps )
jcnd.2
|- ( ph -> -. ch )
Assertion jcnd
|- ( ph -> -. ( ps -> ch ) )

Proof

Step Hyp Ref Expression
1 jcnd.1
 |-  ( ph -> ps )
2 jcnd.2
 |-  ( ph -> -. ch )
3 jcn
 |-  ( ps -> ( -. ch -> -. ( ps -> ch ) ) )
4 1 2 3 sylc
 |-  ( ph -> -. ( ps -> ch ) )