Metamath Proof Explorer


Theorem ad3antrrr

Description: Deduction adding three conjuncts to antecedent. (Contributed by NM, 28-Jul-2012)

Ref Expression
Hypothesis ad2ant.1
|- ( ph -> ps )
Assertion ad3antrrr
|- ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) -> ps )

Proof

Step Hyp Ref Expression
1 ad2ant.1
 |-  ( ph -> ps )
2 1 adantr
 |-  ( ( ph /\ ch ) -> ps )
3 2 ad2antrr
 |-  ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) -> ps )