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| 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 2182. (Contributed by BJ, 28-Jul-2023.) The proof should not rely on df-nf 1783 except via df-nf 1783 directly. (Proof modification is discouraged.) | 
| Ref | Expression | 
|---|---|
| bj-nfnnfTEMP | ⊢ (Ⅎ'𝑥𝜑 ↔ Ⅎ𝑥𝜑) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | bj-dfnnf3 36759 | . 2 ⊢ (Ⅎ'𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑)) | |
| 2 | df-nf 1783 | . 2 ⊢ (Ⅎ𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑)) | |
| 3 | 1, 2 | bitr4i 278 | 1 ⊢ (Ⅎ'𝑥𝜑 ↔ Ⅎ𝑥𝜑) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ↔ wb 206 ∀wal 1537 ∃wex 1778 Ⅎwnf 1782 Ⅎ'wnnf 36725 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-12 2176 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1779 df-nf 1783 df-bj-nnf 36726 | 
| This theorem is referenced by: (None) | 
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