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Theorem hbra1 2938
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 2937 . 2 𝑥𝑥𝐴 𝜑
21nf5ri 2063 1 (∀𝑥𝐴 𝜑 → ∀𝑥𝑥𝐴 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1478  wral 2908
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-10 2016  ax-12 2044
This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1702  df-nf 1707  df-ral 2913
This theorem is referenced by:  bnj1095  30613  bnj1309  30851  mpt2bi123f  33642  hbra2VD  38618  tratrbVD  38619  ssralv2VD  38624
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