Description: e102 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ee102.1 | |- ( ph -> ps ) |
|
ee102.2 | |- ch |
||
ee102.3 | |- ( ph -> ( th -> ta ) ) |
||
ee102.4 | |- ( ps -> ( ch -> ( ta -> et ) ) ) |
||
Assertion | ee102 | |- ( ph -> ( th -> et ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ee102.1 | |- ( ph -> ps ) |
|
2 | ee102.2 | |- ch |
|
3 | ee102.3 | |- ( ph -> ( th -> ta ) ) |
|
4 | ee102.4 | |- ( ps -> ( ch -> ( ta -> et ) ) ) |
|
5 | 1 | a1d | |- ( ph -> ( th -> ps ) ) |
6 | 2 | a1i | |- ( th -> ch ) |
7 | 6 | a1i | |- ( ph -> ( th -> ch ) ) |
8 | 5 7 3 4 | ee222 | |- ( ph -> ( th -> et ) ) |