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Theorem alral 2672
Description: Universal quantification implies restricted quantification. (Contributed by NM, 20-Oct-2006.)
Assertion
Ref Expression
alral (xφx A φ)

Proof of Theorem alral
StepHypRef Expression
1 ax-1 6 . . 3 (φ → (x Aφ))
21alimi 1559 . 2 (xφx(x Aφ))
3 df-ral 2619 . 2 (x A φx(x Aφ))
42, 3sylibr 203 1 (xφx A φ)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1540   wcel 1710  wral 2614
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557
This theorem depends on definitions:  df-bi 177  df-ral 2619
This theorem is referenced by: (None)
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