Theorem hbra1 3275

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 3262	. 2 ⊢ Ⅎ𝑥∀𝑥 ∈ 𝐴 𝜑
2	1	nf5ri 2203	1 ⊢ (∀𝑥 ∈ 𝐴 𝜑 → ∀𝑥∀𝑥 ∈ 𝐴 𝜑)

Syntax hints:   → wi 4  ∀wal 1540  ∀wral 3052

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-10 2147  ax-12 2185

This theorem depends on definitions:  df-bi 207  df-or 849  df-ex 1782  df-nf 1786  df-ral 3053

This theorem is referenced by:  bnj1095  34958  bnj1309  35198  mpobi123f  38413  hbra2VD  45215  tratrbVD  45216  ssralv2VD  45221