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Theorem hbra1 3220
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 3219 . 2 𝑥𝑥𝐴 𝜑
21nf5ri 2191 1 (∀𝑥𝐴 𝜑 → ∀𝑥𝑥𝐴 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1531  wral 3138
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-10 2141  ax-12 2173
This theorem depends on definitions:  df-bi 209  df-or 844  df-ex 1777  df-nf 1781  df-ral 3143
This theorem is referenced by:  bnj1095  32053  bnj1309  32294  mpobi123f  35439  hbra2VD  41192  tratrbVD  41193  ssralv2VD  41198
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