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Mirrors > Home > ILE Home > Th. List > ax-ial | GIF version |
Description: 𝑥 is not free in ∀𝑥𝜑. One of the axioms of predicate logic. (Contributed by Mario Carneiro, 31-Jan-2015.) |
Ref | Expression |
---|---|
ax-ial | ⊢ (∀𝑥𝜑 → ∀𝑥∀𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph | . . 3 wff 𝜑 | |
2 | vx | . . 3 setvar 𝑥 | |
3 | 1, 2 | wal 1333 | . 2 wff ∀𝑥𝜑 |
4 | 3, 2 | wal 1333 | . 2 wff ∀𝑥∀𝑥𝜑 |
5 | 3, 4 | wi 4 | 1 wff (∀𝑥𝜑 → ∀𝑥∀𝑥𝜑) |
Colors of variables: wff set class |
This axiom is referenced by: hba1 1520 ax6b 1631 exdistrfor 1780 sbcof2 1790 hbs1 1918 sbcomxyyz 1952 |
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