Description: e21an without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ee21an.1 | |- ( ph -> ( ps -> ch ) ) |
|
ee21an.2 | |- ( ph -> th ) |
||
ee21an.3 | |- ( ( ch /\ th ) -> ta ) |
||
Assertion | ee21an | |- ( ph -> ( ps -> ta ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ee21an.1 | |- ( ph -> ( ps -> ch ) ) |
|
2 | ee21an.2 | |- ( ph -> th ) |
|
3 | ee21an.3 | |- ( ( ch /\ th ) -> ta ) |
|
4 | 3 | ex | |- ( ch -> ( th -> ta ) ) |
5 | 1 2 4 | syl6ci | |- ( ph -> ( ps -> ta ) ) |