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Theorem hbsbv 1817
 Description: This is a version of hbsb 1823 with an extra distinct variable constraint, on and . (Contributed by Jim Kingdon, 25-Dec-2017.)
Hypothesis
Ref Expression
hbsbv.1
Assertion
Ref Expression
hbsbv
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)

Proof of Theorem hbsbv
StepHypRef Expression
1 df-sb 1646 . 2
2 ax-17 1419 . . . 4
3 hbsbv.1 . . . 4
42, 3hbim 1437 . . 3
52, 3hban 1439 . . . 4
65hbex 1527 . . 3
74, 6hban 1439 . 2
81, 7hbxfrbi 1361 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97  wal 1241  wex 1381  wsb 1645 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 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-sb 1646 This theorem is referenced by:  sbco2vlem  1820  2sb5rf  1865  2sb6rf  1866
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