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Theorem bnj946 32325
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj946.1 (𝜑 ↔ ∀𝑥𝐴 𝜓)
Assertion
Ref Expression
bnj946 (𝜑 ↔ ∀𝑥(𝑥𝐴𝜓))

Proof of Theorem bnj946
StepHypRef Expression
1 bnj946.1 . 2 (𝜑 ↔ ∀𝑥𝐴 𝜓)
2 df-ral 3058 . 2 (∀𝑥𝐴 𝜓 ↔ ∀𝑥(𝑥𝐴𝜓))
31, 2bitri 278 1 (𝜑 ↔ ∀𝑥(𝑥𝐴𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209  wal 1540  wcel 2113  wral 3053
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 210  df-ral 3058
This theorem is referenced by:  bnj1379  32381  bnj570  32456  bnj571  32457
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