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Theorem hbxfreq 2141
 Description: A utility lemma to transfer a bound-variable hypothesis builder into a definition. See hbxfrbi 1358 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 2101 . 2 (y Ay B)
3 hbxfr.2 . 2 (y Bx y B)
42, 3hbxfrbi 1358 1 (y Ax y A)
 Colors of variables: wff set class Syntax hints:   → wi 4  ∀wal 1240   = wceq 1242   ∈ wcel 1390 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-clel 2033 This theorem is referenced by: (None)
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