Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > nfrOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of nf5r 2052 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 1712 | . 2 ⊢ (Ⅎ𝑥𝜑 ↔ ∀𝑥(𝜑 → ∀𝑥𝜑)) | |
2 | sp 2041 | . 2 ⊢ (∀𝑥(𝜑 → ∀𝑥𝜑) → (𝜑 → ∀𝑥𝜑)) | |
3 | 1, 2 | sylbi 206 | 1 ⊢ (Ⅎ𝑥𝜑 → (𝜑 → ∀𝑥𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1473 ℲwnfOLD 1700 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-12 2034 |
This theorem depends on definitions: df-bi 196 df-ex 1696 df-nfOLD 1712 |
This theorem is referenced by: nfriOLD 2177 nfrdOLD 2178 19.21t-1OLD 2200 nfimdOLD 2214 |
Copyright terms: Public domain | W3C validator |