Description: A wff is equivalent to its equivalence with a truth. (Contributed by NM, 18-Aug-1993) (Proof shortened by Andrew Salmon, 13-May-2011)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | tbt.1 | |- ph |
|
| Assertion | tbt | |- ( ps <-> ( ps <-> ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | tbt.1 | |- ph |
|
| 2 | ibibr | |- ( ( ph -> ps ) <-> ( ph -> ( ps <-> ph ) ) ) |
|
| 3 | 2 | pm5.74ri | |- ( ph -> ( ps <-> ( ps <-> ph ) ) ) |
| 4 | 1 3 | ax-mp | |- ( ps <-> ( ps <-> ph ) ) |