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Mirrors > Home > MPE Home > Th. List > nfbii | Structured version Visualization version GIF version |
Description: Equality theorem for the non-freeness predicate. (Contributed by Mario Carneiro, 11-Aug-2016.) df-nf 1880 changed. (Revised by Wolf Lammen, 12-Sep-2021.) |
Ref | Expression |
---|---|
nfbii.1 | ⊢ (𝜑 ↔ 𝜓) |
Ref | Expression |
---|---|
nfbii | ⊢ (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfbiit 1947 | . 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓)) | |
2 | nfbii.1 | . 2 ⊢ (𝜑 ↔ 𝜓) | |
3 | 1, 2 | mpg 1893 | 1 ⊢ (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 198 Ⅎwnf 1879 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1891 ax-4 1905 |
This theorem depends on definitions: df-bi 199 df-ex 1876 df-nf 1880 |
This theorem is referenced by: nfxfr 1949 nfxfrd 1950 dvelimhw 2360 nfeqf1 2387 dfnfc2 4649 bj-dvelimdv1 33328 bj-nfcf 33412 iunconnlem2 39926 |
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