Metamath Proof Explorer


Theorem anim1d

Description: Add a conjunct to right of antecedent and consequent in a deduction. (Contributed by NM, 3-Apr-1994)

Ref Expression
Hypothesis anim1d.1
|- ( ph -> ( ps -> ch ) )
Assertion anim1d
|- ( ph -> ( ( ps /\ th ) -> ( ch /\ th ) ) )

Proof

Step Hyp Ref Expression
1 anim1d.1
 |-  ( ph -> ( ps -> ch ) )
2 idd
 |-  ( ph -> ( th -> th ) )
3 1 2 anim12d
 |-  ( ph -> ( ( ps /\ th ) -> ( ch /\ th ) ) )