Description: More general version of 3imtr3i . Useful for converting definitions in a formula. (Contributed by NM, 20-May-1996) (Proof shortened by Wolf Lammen, 20-Dec-2013)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | 3imtr3g.1 | |- ( ph -> ( ps -> ch ) ) |
|
| 3imtr3g.2 | |- ( ps <-> th ) |
||
| 3imtr3g.3 | |- ( ch <-> ta ) |
||
| Assertion | 3imtr3g | |- ( ph -> ( th -> ta ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 3imtr3g.1 | |- ( ph -> ( ps -> ch ) ) |
|
| 2 | 3imtr3g.2 | |- ( ps <-> th ) |
|
| 3 | 3imtr3g.3 | |- ( ch <-> ta ) |
|
| 4 | 2 1 | syl5bir | |- ( ph -> ( th -> ch ) ) |
| 5 | 4 3 | syl6ib | |- ( ph -> ( th -> ta ) ) |