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Theorem hbral 2662
 Description: Bound-variable hypothesis builder for restricted quantification. (Contributed by NM, 1-Sep-1999.) (Revised by David Abernethy, 13-Dec-2009.)
Hypotheses
Ref Expression
hbral.1 (y Ax y A)
hbral.2 (φxφ)
Assertion
Ref Expression
hbral (y A φxy A φ)

Proof of Theorem hbral
StepHypRef Expression
1 df-ral 2619 . 2 (y A φy(y Aφ))
2 hbral.1 . . . 4 (y Ax y A)
3 hbral.2 . . . 4 (φxφ)
42, 3hbim 1817 . . 3 ((y Aφ) → x(y Aφ))
54hbal 1736 . 2 (y(y Aφ) → xy(y Aφ))
61, 5hbxfrbi 1568 1 (y A φxy 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-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545  df-ral 2619 This theorem is referenced by: (None)
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