Metamath Proof Explorer


Theorem simprld

Description: Deduction eliminating a double conjunct. (Contributed by Glauco Siliprandi, 11-Dec-2019)

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

Proof

Step Hyp Ref Expression
1 simprld.1
 |-  ( ph -> ( ps /\ ( ch /\ th ) ) )
2 1 simprd
 |-  ( ph -> ( ch /\ th ) )
3 2 simpld
 |-  ( ph -> ch )