Metamath Proof Explorer


Theorem ancld

Description: Deduction conjoining antecedent to left of consequent in nested implication. (Contributed by NM, 15-Aug-1994) (Proof shortened by Wolf Lammen, 1-Nov-2012)

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

Proof

Step Hyp Ref Expression
1 ancld.1
 |-  ( ph -> ( ps -> ch ) )
2 idd
 |-  ( ph -> ( ps -> ps ) )
3 2 1 jcad
 |-  ( ph -> ( ps -> ( ps /\ ch ) ) )