| Linear Logic Proof Explorer |
< Previous
Next >
Nearby theorems |
|
| Mirrors > Home > LLPE Home > Th. List > ax-alcom | Structured version | |
| Description: Quantifier commutation. |
| Ref | Expression |
|---|---|
| ax-alcom | ⊦ (∀x∀y𝜑 ⊸ ∀y∀x𝜑) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | wph | . . . 4 wff 𝜑 | |
| 2 | vy | . . . 4 var y | |
| 3 | 1, 2 | wal 318 | . . 3 wff ∀y𝜑 |
| 4 | vx | . . 3 var x | |
| 5 | 3, 4 | wal 318 | . 2 wff ∀x∀y𝜑 |
| 6 | 1, 4 | wal 318 | . . 3 wff ∀x𝜑 |
| 7 | 6, 2 | wal 318 | . 2 wff ∀y∀x𝜑 |
| 8 | 5, 7 | wli 61 | 1 wff (∀x∀y𝜑 ⊸ ∀y∀x𝜑) |
| Colors of variables: wff var nilad |
| This axiom is referenced by: (None) |
| Copyright terms: Public domain | W3C validator |