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Axiom ax-wl-11v 32540
Description: Version of ax-11 2021 with distinct variable conditions. Currently implemented as an axiom to detect unintended references to the foundational axiom ax-11 2021. It will later be converted into a theorem directly based on ax-11 2021. (Contributed by Wolf Lammen, 28-Jun-2019.)
Assertion
Ref Expression
ax-wl-11v (∀𝑥𝑦𝜑 → ∀𝑦𝑥𝜑)
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)

Detailed syntax breakdown of Axiom ax-wl-11v
StepHypRef Expression
1 wph . . . 4 wff 𝜑
2 vy . . . 4 setvar 𝑦
31, 2wal 1473 . . 3 wff 𝑦𝜑
4 vx . . 3 setvar 𝑥
53, 4wal 1473 . 2 wff 𝑥𝑦𝜑
61, 4wal 1473 . . 3 wff 𝑥𝜑
76, 2wal 1473 . 2 wff 𝑦𝑥𝜑
85, 7wi 4 1 wff (∀𝑥𝑦𝜑 → ∀𝑦𝑥𝜑)
Colors of variables: wff setvar class
This axiom is referenced by:  wl-ax11-lem3  32543  wl-ax11-lem6  32546
  Copyright terms: Public domain W3C validator