Description: e112 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
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Hypotheses | ee112.1 | |- ( ph -> ps ) |
|
ee112.2 | |- ( ph -> ch ) |
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ee112.3 | |- ( ph -> ( th -> ta ) ) |
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ee112.4 | |- ( ps -> ( ch -> ( ta -> et ) ) ) |
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Assertion | ee112 | |- ( ph -> ( th -> et ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ee112.1 | |- ( ph -> ps ) |
|
2 | ee112.2 | |- ( ph -> ch ) |
|
3 | ee112.3 | |- ( ph -> ( th -> ta ) ) |
|
4 | ee112.4 | |- ( ps -> ( ch -> ( ta -> et ) ) ) |
|
5 | 1 | a1d | |- ( ph -> ( th -> ps ) ) |
6 | 2 | a1d | |- ( ph -> ( th -> ch ) ) |
7 | 5 6 3 4 | ee222 | |- ( ph -> ( th -> et ) ) |