Description: syl2an with antecedents in standard conjunction form. (Contributed by Alan Sare, 27-Aug-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | eel3132.1 | |- ( ( ph /\ ps ) -> ch ) |
|
eel3132.2 | |- ( ( th /\ ps ) -> ta ) |
||
eel3132.3 | |- ( ( ch /\ ta ) -> et ) |
||
Assertion | eel3132 | |- ( ( ph /\ th /\ ps ) -> et ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eel3132.1 | |- ( ( ph /\ ps ) -> ch ) |
|
2 | eel3132.2 | |- ( ( th /\ ps ) -> ta ) |
|
3 | eel3132.3 | |- ( ( ch /\ ta ) -> et ) |
|
4 | 1 2 3 | syl2an | |- ( ( ( ph /\ ps ) /\ ( th /\ ps ) ) -> et ) |
5 | 4 | 3impdir | |- ( ( ph /\ th /\ ps ) -> et ) |