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Theorem hboprab 5562
 Description: Bound-variable hypothesis builder for an operation class abstraction. (Contributed by set.mm contributors, 22-Aug-2013.)
Hypothesis
Ref Expression
hboprab.1
Assertion
Ref Expression
hboprab
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,,,)

Proof of Theorem hboprab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-oprab 5528 . 2
2 ax-17 1616 . . . . . . 7
3 hboprab.1 . . . . . . 7
42, 3hban 1828 . . . . . 6
54hbex 1841 . . . . 5
65hbex 1841 . . . 4
76hbex 1841 . . 3
87hbab 2344 . 2
91, 8hbxfreq 2456 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358  wal 1540  wex 1541   wceq 1642   wcel 1710  cab 2339  cop 4561  coprab 5527 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-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-oprab 5528 This theorem is referenced by: (None)
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