Metamath Proof Explorer

Theorem adantrr

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 4-May-1994) (Proof shortened by Wolf Lammen, 24-Nov-2012)

Ref Expression
Hypothesis adant2.1 
|- ( ( ph /\ ps ) -> ch )
Assertion adantrr 
|- ( ( ph /\ ( ps /\ th ) ) -> ch )

Proof

Step Hyp Ref Expression
1 adant2.1 
 |-  ( ( ph /\ ps ) -> ch )
2 simpl 
 |-  ( ( ps /\ th ) -> ps )
3 2 1 sylan2 
 |-  ( ( ph /\ ( ps /\ th ) ) -> ch )