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 ) ) ) |
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 ) ) ) |