Metamath Proof Explorer


Theorem adantrlr

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004) (Proof shortened by Wolf Lammen, 4-Dec-2012)

Ref Expression
Hypothesis adantr2.1
|- ( ( ph /\ ( ps /\ ch ) ) -> th )
Assertion adantrlr
|- ( ( ph /\ ( ( ps /\ ta ) /\ ch ) ) -> th )

Proof

Step Hyp Ref Expression
1 adantr2.1
 |-  ( ( ph /\ ( ps /\ ch ) ) -> th )
2 simpl
 |-  ( ( ps /\ ta ) -> ps )
3 2 1 sylanr1
 |-  ( ( ph /\ ( ( ps /\ ta ) /\ ch ) ) -> th )