Metamath Proof Explorer


Theorem adantlll

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004) (Proof shortened by Wolf Lammen, 2-Dec-2012)

Ref Expression
Hypothesis adantl2.1
|- ( ( ( ph /\ ps ) /\ ch ) -> th )
Assertion adantlll
|- ( ( ( ( ta /\ ph ) /\ ps ) /\ ch ) -> th )

Proof

Step Hyp Ref Expression
1 adantl2.1
 |-  ( ( ( ph /\ ps ) /\ ch ) -> th )
2 simpr
 |-  ( ( ta /\ ph ) -> ph )
3 2 1 sylanl1
 |-  ( ( ( ( ta /\ ph ) /\ ps ) /\ ch ) -> th )