Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > df-nfOLD | Structured version Visualization version GIF version |
Description: Obsolete definition replaced by nf5 2102 as of 3-Oct-2021. This definition is less suitable than df-nf 1701 when ax-10 2006 and ax-12 2034 are not in effect. (Contributed by Mario Carneiro, 11-Aug-2016.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-nfOLD | ⊢ (Ⅎ𝑥𝜑 ↔ ∀𝑥(𝜑 → ∀𝑥𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph | . . 3 wff 𝜑 | |
2 | vx | . . 3 setvar 𝑥 | |
3 | 1, 2 | wnfOLD 1700 | . 2 wff Ⅎ𝑥𝜑 |
4 | 1, 2 | wal 1473 | . . . 4 wff ∀𝑥𝜑 |
5 | 1, 4 | wi 4 | . . 3 wff (𝜑 → ∀𝑥𝜑) |
6 | 5, 2 | wal 1473 | . 2 wff ∀𝑥(𝜑 → ∀𝑥𝜑) |
7 | 3, 6 | wb 195 | 1 wff (Ⅎ𝑥𝜑 ↔ ∀𝑥(𝜑 → ∀𝑥𝜑)) |
Colors of variables: wff setvar class |
This definition is referenced by: nfiOLD 1725 nfbiiOLD 1824 nfdvOLD 1860 nfrOLD 2176 nfdOLD 2181 nfbidfOLD 2189 19.9dOLD 2191 nfnf1OLDOLD 2196 nfntOLD 2197 nfimdOLD 2214 |
Copyright terms: Public domain | W3C validator |