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Theorem bnj1211 32785
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1211.1 (𝜑 → ∀𝑥𝐴 𝜓)
Assertion
Ref Expression
bnj1211 (𝜑 → ∀𝑥(𝑥𝐴𝜓))

Proof of Theorem bnj1211
StepHypRef Expression
1 bnj1211.1 . 2 (𝜑 → ∀𝑥𝐴 𝜓)
2 df-ral 3069 . 2 (∀𝑥𝐴 𝜓 ↔ ∀𝑥(𝑥𝐴𝜓))
31, 2sylib 217 1 (𝜑 → ∀𝑥(𝑥𝐴𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1537  wcel 2106  wral 3064
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 206  df-ral 3069
This theorem is referenced by:  bnj1533  32840  bnj1204  33000  bnj1523  33059
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