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Theorem hbra1 3290
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 3273 . 2 𝑥𝑥𝐴 𝜑
21nf5ri 2180 1 (∀𝑥𝐴 𝜑 → ∀𝑥𝑥𝐴 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1531  wral 3053
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-10 2129  ax-12 2163
This theorem depends on definitions:  df-bi 206  df-or 845  df-ex 1774  df-nf 1778  df-ral 3054
This theorem is referenced by:  bnj1095  34310  bnj1309  34551  mpobi123f  37533  hbra2VD  44170  tratrbVD  44171  ssralv2VD  44176
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