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Theorem hbxfreq 2456
 Description: A utility lemma to transfer a bound-variable hypothesis builder into a definition. See hbxfrbi 1568 for equivalence version. (Contributed by NM, 21-Aug-2007.)
Hypotheses
Ref Expression
hbxfr.1 A = B
hbxfr.2 (y Bx y B)
Assertion
Ref Expression
hbxfreq (y Ax y A)

Proof of Theorem hbxfreq
StepHypRef Expression
1 hbxfr.1 . . 3 A = B
21eleq2i 2417 . 2 (y Ay B)
3 hbxfr.2 . 2 (y Bx y B)
42, 3hbxfrbi 1568 1 (y Ax y A)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1540   = wceq 1642   ∈ wcel 1710 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-cleq 2346  df-clel 2349 This theorem is referenced by:  hboprab1  5559  hboprab2  5560  hboprab3  5561  hboprab  5562
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