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Axiom ax-ial 1468
Description: 𝑥 is not free in 𝑥𝜑. One of the axioms of predicate logic. (Contributed by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
ax-ial (∀𝑥𝜑 → ∀𝑥𝑥𝜑)

Detailed syntax breakdown of Axiom ax-ial
StepHypRef Expression
1 wph . . 3 wff 𝜑
2 vx . . 3 setvar 𝑥
31, 2wal 1283 . 2 wff 𝑥𝜑
43, 2wal 1283 . 2 wff 𝑥𝑥𝜑
53, 4wi 4 1 wff (∀𝑥𝜑 → ∀𝑥𝑥𝜑)
Colors of variables: wff set class
This axiom is referenced by:  hba1  1474  ax6b  1582  exdistrfor  1723  sbcof2  1733  hbs1  1857  sbcomxyyz  1889
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