Description: Obsolete version of drnfc2 as of 22-Sep-2024. (Contributed by Mario Carneiro, 8-Oct-2016) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | drnfc1.1 | |- ( A. x x = y -> A = B ) |
|
| Assertion | drnfc2OLD | |- ( A. x x = y -> ( F/_ z A <-> F/_ z B ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | drnfc1.1 | |- ( A. x x = y -> A = B ) |
|
| 2 | 1 | eleq2d | |- ( A. x x = y -> ( w e. A <-> w e. B ) ) |
| 3 | 2 | drnf2 | |- ( A. x x = y -> ( F/ z w e. A <-> F/ z w e. B ) ) |
| 4 | 3 | albidv | |- ( A. x x = y -> ( A. w F/ z w e. A <-> A. w F/ z w e. B ) ) |
| 5 | df-nfc | |- ( F/_ z A <-> A. w F/ z w e. A ) |
|
| 6 | df-nfc | |- ( F/_ z B <-> A. w F/ z w e. B ) |
|
| 7 | 4 5 6 | 3bitr4g | |- ( A. x x = y -> ( F/_ z A <-> F/_ z B ) ) |