Metamath Proof Explorer


Theorem jctr

Description: Inference conjoining a theorem to the right of a consequent. (Contributed by NM, 18-Aug-1993) (Proof shortened by Wolf Lammen, 24-Oct-2012)

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

Proof

Step Hyp Ref Expression
1 jctl.1
 |-  ps
2 id
 |-  ( ph -> ph )
3 2 1 jctir
 |-  ( ph -> ( ph /\ ps ) )