Description: Commutation of antecedents. Swap 4th and 5th. Deduction associated with com34 . Double deduction associated with com23 . Triple deduction associated with com12 . (Contributed by Jeff Hankins, 28-Jun-2009)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | com5.1 | |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) ) |
|
| Assertion | com45 | |- ( ph -> ( ps -> ( ch -> ( ta -> ( th -> et ) ) ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | com5.1 | |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) ) |
|
| 2 | pm2.04 | |- ( ( th -> ( ta -> et ) ) -> ( ta -> ( th -> et ) ) ) |
|
| 3 | 1 2 | syl8 | |- ( ph -> ( ps -> ( ch -> ( ta -> ( th -> et ) ) ) ) ) |