Description: syl2an with antecedents in standard conjunction form. (Contributed by Alan Sare, 26-Aug-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | eel132.1 | |- ( ph -> ps ) |
|
eel132.2 | |- ( ( ch /\ th ) -> ta ) |
||
eel132.3 | |- ( ( ps /\ ta ) -> et ) |
||
Assertion | eel132 | |- ( ( ph /\ ch /\ th ) -> et ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eel132.1 | |- ( ph -> ps ) |
|
2 | eel132.2 | |- ( ( ch /\ th ) -> ta ) |
|
3 | eel132.3 | |- ( ( ps /\ ta ) -> et ) |
|
4 | 1 2 3 | syl2an | |- ( ( ph /\ ( ch /\ th ) ) -> et ) |
5 | 4 | 3impb | |- ( ( ph /\ ch /\ th ) -> et ) |