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Mirrors > Home > MPE Home > Th. List > nfrOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of nf5r 2218 as of 6-Oct-2021. (Contributed by Mario Carneiro, 26-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
nfrOLD | ⊢ (Ⅎ𝑥𝜑 → (𝜑 → ∀𝑥𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nfOLD 1869 | . 2 ⊢ (Ⅎ𝑥𝜑 ↔ ∀𝑥(𝜑 → ∀𝑥𝜑)) | |
2 | sp 2207 | . 2 ⊢ (∀𝑥(𝜑 → ∀𝑥𝜑) → (𝜑 → ∀𝑥𝜑)) | |
3 | 1, 2 | sylbi 207 | 1 ⊢ (Ⅎ𝑥𝜑 → (𝜑 → ∀𝑥𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1629 ℲwnfOLD 1857 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1870 ax-4 1885 ax-5 1991 ax-6 2057 ax-7 2093 ax-12 2203 |
This theorem depends on definitions: df-bi 197 df-ex 1853 df-nfOLD 1869 |
This theorem is referenced by: nfriOLD 2351 nfrdOLD 2352 19.21t-1OLD 2374 nfimdOLD 2388 |
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