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Theorem hbra1 3088
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 3087 . 2 𝑥𝑥𝐴 𝜑
21nf5ri 2227 1 (∀𝑥𝐴 𝜑 → ∀𝑥𝑥𝐴 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1650  wral 3054
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2069  ax-7 2105  ax-10 2183  ax-12 2211
This theorem depends on definitions:  df-bi 198  df-or 874  df-ex 1875  df-nf 1879  df-ral 3059
This theorem is referenced by:  bnj1095  31231  bnj1309  31469  mpt2bi123f  34324  hbra2VD  39680  tratrbVD  39681  ssralv2VD  39686
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