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Metamath Proof Explorer
Description: An inference from transitive law for logical equivalence. (Contributed by NM, 3-Jan-1993) (Proof shortened by Wolf Lammen, 13-Oct-2012)
|
|
Ref |
Expression |
|
Hypotheses |
bitri.1 |
|- ( ph <-> ps ) |
|
|
bitri.2 |
|- ( ps <-> ch ) |
|
Assertion |
bitri |
|- ( ph <-> ch ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
bitri.1 |
|- ( ph <-> ps ) |
| 2 |
|
bitri.2 |
|- ( ps <-> ch ) |
| 3 |
1 2
|
sylbb |
|- ( ph -> ch ) |
| 4 |
1 2
|
sylbbr |
|- ( ch -> ph ) |
| 5 |
3 4
|
impbii |
|- ( ph <-> ch ) |