Description: e121 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | ee121.1 | |- ( ph -> ps ) |
|
| ee121.2 | |- ( ph -> ( ch -> th ) ) |
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| ee121.3 | |- ( ph -> ta ) |
||
| ee121.4 | |- ( ps -> ( th -> ( ta -> et ) ) ) |
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| Assertion | ee121 | |- ( ph -> ( ch -> et ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ee121.1 | |- ( ph -> ps ) |
|
| 2 | ee121.2 | |- ( ph -> ( ch -> th ) ) |
|
| 3 | ee121.3 | |- ( ph -> ta ) |
|
| 4 | ee121.4 | |- ( ps -> ( th -> ( ta -> et ) ) ) |
|
| 5 | 1 | a1d | |- ( ph -> ( ch -> ps ) ) |
| 6 | 3 | a1d | |- ( ph -> ( ch -> ta ) ) |
| 7 | 5 2 6 4 | ee222 | |- ( ph -> ( ch -> et ) ) |