Description: Value of the conditional operator for propositions when its first argument is false. Analogue for propositions of iffalse . This is essentially dedlemb . (Contributed by BJ, 20-Sep-2019) (Proof shortened by Wolf Lammen, 25-Jun-2020)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | ifpfal | |- ( -. ph -> ( if- ( ph , ps , ch ) <-> ch ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ifpn | |- ( if- ( ph , ps , ch ) <-> if- ( -. ph , ch , ps ) ) |
|
| 2 | ifptru | |- ( -. ph -> ( if- ( -. ph , ch , ps ) <-> ch ) ) |
|
| 3 | 1 2 | syl5bb | |- ( -. ph -> ( if- ( ph , ps , ch ) <-> ch ) ) |