Description: Obsolete version of had1 as of 10-Aug-2026. (Contributed by Mario Carneiro, 4-Sep-2016) (Proof shortened by Wolf Lammen, 11-Jul-2020) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | had1OLD | |- ( ph -> ( hadd ( ph , ps , ch ) <-> ( ps <-> ch ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | hadrot | |- ( hadd ( ph , ps , ch ) <-> hadd ( ps , ch , ph ) ) |
|
| 2 | hadbi | |- ( hadd ( ps , ch , ph ) <-> ( ( ps <-> ch ) <-> ph ) ) |
|
| 3 | 1 2 | bitri | |- ( hadd ( ph , ps , ch ) <-> ( ( ps <-> ch ) <-> ph ) ) |
| 4 | biass | |- ( ( ( hadd ( ph , ps , ch ) <-> ( ps <-> ch ) ) <-> ph ) <-> ( hadd ( ph , ps , ch ) <-> ( ( ps <-> ch ) <-> ph ) ) ) |
|
| 5 | 3 4 | mpbir | |- ( ( hadd ( ph , ps , ch ) <-> ( ps <-> ch ) ) <-> ph ) |
| 6 | 5 | biimpri | |- ( ph -> ( hadd ( ph , ps , ch ) <-> ( ps <-> ch ) ) ) |