![]() |
Mathbox for BJ |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nfnnfTEMP | Structured version Visualization version GIF version |
Description: New nonfreeness is equivalent to old nonfreeness on core FOL axioms plus sp 2169. (Contributed by BJ, 28-Jul-2023.) The proof should not rely on df-nf 1779 except via df-nf 1779 directly. (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-nfnnfTEMP | ⊢ (Ⅎ'𝑥𝜑 ↔ Ⅎ𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-dfnnf3 36157 | . 2 ⊢ (Ⅎ'𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑)) | |
2 | df-nf 1779 | . 2 ⊢ (Ⅎ𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑)) | |
3 | 1, 2 | bitr4i 278 | 1 ⊢ (Ⅎ'𝑥𝜑 ↔ Ⅎ𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 ∀wal 1532 ∃wex 1774 Ⅎwnf 1778 Ⅎ'wnnf 36123 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-12 2164 |
This theorem depends on definitions: df-bi 206 df-an 396 df-ex 1775 df-nf 1779 df-bj-nnf 36124 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |