Metamath Proof Explorer


Theorem anim12ii

Description: Conjoin antecedents and consequents in a deduction. (Contributed by NM, 11-Nov-2007) (Proof shortened by Wolf Lammen, 19-Jul-2013)

Ref Expression
Hypotheses anim12ii.1
|- ( ph -> ( ps -> ch ) )
anim12ii.2
|- ( th -> ( ps -> ta ) )
Assertion anim12ii
|- ( ( ph /\ th ) -> ( ps -> ( ch /\ ta ) ) )

Proof

Step Hyp Ref Expression
1 anim12ii.1
 |-  ( ph -> ( ps -> ch ) )
2 anim12ii.2
 |-  ( th -> ( ps -> ta ) )
3 pm3.43
 |-  ( ( ( ps -> ch ) /\ ( ps -> ta ) ) -> ( ps -> ( ch /\ ta ) ) )
4 1 2 3 syl2an
 |-  ( ( ph /\ th ) -> ( ps -> ( ch /\ ta ) ) )