Description: Obsolete version of ifpn as of 5-May-2024. (Contributed by BJ, 30-Sep-2019) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | ifpnOLD | |- ( if- ( ph , ps , ch ) <-> if- ( -. ph , ch , ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | notnotb | |- ( ph <-> -. -. ph ) |
|
| 2 | 1 | imbi1i | |- ( ( ph -> ps ) <-> ( -. -. ph -> ps ) ) |
| 3 | 2 | anbi2ci | |- ( ( ( ph -> ps ) /\ ( -. ph -> ch ) ) <-> ( ( -. ph -> ch ) /\ ( -. -. ph -> ps ) ) ) |
| 4 | dfifp2 | |- ( if- ( ph , ps , ch ) <-> ( ( ph -> ps ) /\ ( -. ph -> ch ) ) ) |
|
| 5 | dfifp2 | |- ( if- ( -. ph , ch , ps ) <-> ( ( -. ph -> ch ) /\ ( -. -. ph -> ps ) ) ) |
|
| 6 | 3 4 5 | 3bitr4i | |- ( if- ( ph , ps , ch ) <-> if- ( -. ph , ch , ps ) ) |