Theorem hbra1 3284

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 3269	. 2 ⊢ Ⅎ𝑥∀𝑥 ∈ 𝐴 𝜑
2	1	nf5ri 2194	1 ⊢ (∀𝑥 ∈ 𝐴 𝜑 → ∀𝑥∀𝑥 ∈ 𝐴 𝜑)

Syntax hints:   → wi 4  ∀wal 1537  ∀wral 3050

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-10 2140  ax-12 2176

This theorem depends on definitions:  df-bi 207  df-or 848  df-ex 1779  df-nf 1783  df-ral 3051

This theorem is referenced by:  bnj1095  34754  bnj1309  34995  mpobi123f  38128  hbra2VD  44837  tratrbVD  44838  ssralv2VD  44843