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Theorem bnj1095 29908
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1095.1 (𝜑 ↔ ∀𝑥𝐴 𝜓)
Assertion
Ref Expression
bnj1095 (𝜑 → ∀𝑥𝜑)

Proof of Theorem bnj1095
StepHypRef Expression
1 bnj1095.1 . 2 (𝜑 ↔ ∀𝑥𝐴 𝜓)
2 hbra1 2921 . 2 (∀𝑥𝐴 𝜓 → ∀𝑥𝑥𝐴 𝜓)
31, 2hbxfrbi 1740 1 (𝜑 → ∀𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  wal 1472  wral 2891
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726  ax-5 1825  ax-6 1873  ax-7 1920  ax-10 2004  ax-12 2031
This theorem depends on definitions:  df-bi 195  df-or 383  df-ex 1695  df-nf 1700  df-ral 2896
This theorem is referenced by:  bnj1379  29957  bnj605  30033  bnj594  30038  bnj607  30042  bnj911  30058  bnj964  30069  bnj983  30077  bnj1093  30104  bnj1123  30110  bnj1145  30117  bnj1417  30165
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