Metamath Proof Explorer

Theorem 3anim1i

Description: Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 16-Aug-2009)

Ref Expression
Hypothesis 3animi.1 
|- ( ph -> ps )
Assertion 3anim1i 
|- ( ( ph /\ ch /\ th ) -> ( ps /\ ch /\ th ) )

Proof

Step Hyp Ref Expression
1 3animi.1 
 |-  ( ph -> ps )
2 id 
 |-  ( ch -> ch )
3 id 
 |-  ( th -> th )
4 1 2 3 3anim123i 
 |-  ( ( ph /\ ch /\ th ) -> ( ps /\ ch /\ th ) )