Metamath Proof Explorer


Theorem mpi

Description: A nested modus ponens inference. Inference associated with com12 . (Contributed by NM, 29-Dec-1992) (Proof shortened by Stefan Allan, 20-Mar-2006)

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

Proof

Step Hyp Ref Expression
1 mpi.1
 |-  ps
2 mpi.2
 |-  ( ph -> ( ps -> ch ) )
3 1 a1i
 |-  ( ph -> ps )
4 3 2 mpd
 |-  ( ph -> ch )