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Theorem hbra1 2397
Description: 𝑥 is not free in 𝑥𝐴𝜑. (Contributed by NM, 18-Oct-1996.)
Assertion
Ref Expression
hbra1 (∀𝑥𝐴 𝜑 → ∀𝑥𝑥𝐴 𝜑)

Proof of Theorem hbra1
StepHypRef Expression
1 df-ral 2354 . 2 (∀𝑥𝐴 𝜑 ↔ ∀𝑥(𝑥𝐴𝜑))
2 hba1 1474 . 2 (∀𝑥(𝑥𝐴𝜑) → ∀𝑥𝑥(𝑥𝐴𝜑))
31, 2hbxfrbi 1402 1 (∀𝑥𝐴 𝜑 → ∀𝑥𝑥𝐴 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1283  wcel 1434  wral 2349
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-ral 2354
This theorem is referenced by: (None)
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