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Theorem hbra1 2971
Description: The setvar 𝑥 is not free in 𝑥𝐴𝜑. (Contributed by NM, 18-Oct-1996.) (Proof shortened by Wolf Lammen, 7-Dec-2019.)
Assertion
Ref Expression
hbra1 (∀𝑥𝐴 𝜑 → ∀𝑥𝑥𝐴 𝜑)

Proof of Theorem hbra1
StepHypRef Expression
1 nfra1 2970 . 2 𝑥𝑥𝐴 𝜑
21nf5ri 2103 1 (∀𝑥𝐴 𝜑 → ∀𝑥𝑥𝐴 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1521  wral 2941
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-10 2059  ax-12 2087
This theorem depends on definitions:  df-bi 197  df-or 384  df-ex 1745  df-nf 1750  df-ral 2946
This theorem is referenced by:  bnj1095  30978  bnj1309  31216  mpt2bi123f  34101  hbra2VD  39410  tratrbVD  39411  ssralv2VD  39416
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