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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) |
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