Theorem hbra1 3269

Description: The setvar 𝑥 is not free in ∀𝑥 ∈ 𝐴𝜑. (Contributed by NM, 18-Oct-1996.) (Proof shortened by Wolf Lammen, 7-Dec-2019.)

Assertion

Ref	Expression
hbra1	⊢ (∀𝑥 ∈ 𝐴 𝜑 → ∀𝑥∀𝑥 ∈ 𝐴 𝜑)

Proof of Theorem hbra1

Step	Hyp	Ref	Expression
1		nfra1 3256	. 2 ⊢ Ⅎ𝑥∀𝑥 ∈ 𝐴 𝜑
2	1	nf5ri 2198	1 ⊢ (∀𝑥 ∈ 𝐴 𝜑 → ∀𝑥∀𝑥 ∈ 𝐴 𝜑)

Syntax hints:   → wi 4  ∀wal 1539  ∀wral 3047

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-10 2144  ax-12 2180

This theorem depends on definitions:  df-bi 207  df-or 848  df-ex 1781  df-nf 1785  df-ral 3048

This theorem is referenced by:  bnj1095  34793  bnj1309  35034  mpobi123f  38210  hbra2VD  44900  tratrbVD  44901  ssralv2VD  44906