Mathbox for Wolf Lammen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > ax-wl-11v | Structured version Visualization version GIF version |
Description: Version of ax-11 2160 with distinct variable conditions. Currently implemented as an axiom to detect unintended references to the foundational axiom ax-11 2160. It will later be converted into a theorem directly based on ax-11 2160. (Contributed by Wolf Lammen, 28-Jun-2019.) |
Ref | Expression |
---|---|
ax-wl-11v | ⊢ (∀𝑥∀𝑦𝜑 → ∀𝑦∀𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph | . . . 4 wff 𝜑 | |
2 | vy | . . . 4 setvar 𝑦 | |
3 | 1, 2 | wal 1541 | . . 3 wff ∀𝑦𝜑 |
4 | vx | . . 3 setvar 𝑥 | |
5 | 3, 4 | wal 1541 | . 2 wff ∀𝑥∀𝑦𝜑 |
6 | 1, 4 | wal 1541 | . . 3 wff ∀𝑥𝜑 |
7 | 6, 2 | wal 1541 | . 2 wff ∀𝑦∀𝑥𝜑 |
8 | 5, 7 | wi 4 | 1 wff (∀𝑥∀𝑦𝜑 → ∀𝑦∀𝑥𝜑) |
Colors of variables: wff setvar class |
This axiom is referenced by: wl-ax11-lem3 35507 wl-ax11-lem6 35510 |
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