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Theorem bnj1142 29920
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1142.1 (𝜑 → ∀𝑥(𝑥𝐴𝜓))
Assertion
Ref Expression
bnj1142 (𝜑 → ∀𝑥𝐴 𝜓)

Proof of Theorem bnj1142
StepHypRef Expression
1 bnj1142.1 . 2 (𝜑 → ∀𝑥(𝑥𝐴𝜓))
2 df-ral 2900 . 2 (∀𝑥𝐴 𝜓 ↔ ∀𝑥(𝑥𝐴𝜓))
31, 2sylibr 222 1 (𝜑 → ∀𝑥𝐴 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1472  wcel 1976  wral 2895
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 195  df-ral 2900
This theorem is referenced by:  bnj1476  29977  bnj1533  29982  bnj1523  30199
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