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Axiom ax-ial 1514
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 1329 . 2 wff 𝑥𝜑
43, 2wal 1329 . 2 wff 𝑥𝑥𝜑
53, 4wi 4 1 wff (∀𝑥𝜑 → ∀𝑥𝑥𝜑)
Colors of variables: wff set class
This axiom is referenced by:  hba1  1520  ax6b  1629  exdistrfor  1772  sbcof2  1782  hbs1  1909  sbcomxyyz  1943
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