Theorem axial 2725

Description: The setvar 𝑥 is not free in ∀𝑥𝜑 (intuitionistic logic axiom ax-ial). (Contributed by Jim Kingdon, 31-Dec-2017.) (New usage is discouraged.)

Assertion

Ref	Expression
axial	⊢ (∀𝑥𝜑 → ∀𝑥∀𝑥𝜑)

Proof of Theorem axial

Step	Hyp	Ref	Expression
1		hba1 2326	1 ⊢ (∀𝑥𝜑 → ∀𝑥∀𝑥𝜑)

This proof depends on syntax axioms:   → wi 4  ∀wal 1567

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-10 2177  ax-12 2212

This proof depends on definitions:  df-bi 210  df-or 862  df-ex 1812  df-nf 1816

This theorem is used by: (None)