Description: Deduction joining two biconditionals with different antecedents. (Contributed by NM, 12-May-2004)
Ref | Expression | ||
---|---|---|---|
Hypotheses | bi2an9.1 | |- ( ph -> ( ps <-> ch ) ) |
|
bi2an9.2 | |- ( th -> ( ta <-> et ) ) |
||
Assertion | bi2bian9 | |- ( ( ph /\ th ) -> ( ( ps <-> ta ) <-> ( ch <-> et ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bi2an9.1 | |- ( ph -> ( ps <-> ch ) ) |
|
2 | bi2an9.2 | |- ( th -> ( ta <-> et ) ) |
|
3 | 1 | adantr | |- ( ( ph /\ th ) -> ( ps <-> ch ) ) |
4 | 2 | adantl | |- ( ( ph /\ th ) -> ( ta <-> et ) ) |
5 | 3 4 | bibi12d | |- ( ( ph /\ th ) -> ( ( ps <-> ta ) <-> ( ch <-> et ) ) ) |