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Theorem 19.3v 1755
 Description: Version of 19.3 1888 with a dv condition, requiring fewer axioms. Any formula can be universally quantified using a variable which it does not contain. See also 19.9v 1754. (Contributed by Anthony Hart, 13-Sep-2011.) Remove dependency on ax-7 1790. (Revised by Wolf Lammen, 4-Dec-2017.)
Assertion
Ref Expression
19.3v
Distinct variable group:   ,

Proof of Theorem 19.3v
StepHypRef Expression
1 alex 1647 . 2
2 19.9v 1754 . . 3
32con2bii 332 . 2
41, 3bitr4i 252 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  <->wb 184  A.wal 1393  E.wex 1612 This theorem is referenced by:  spvw  1756  19.27v  1766  19.28v  1767  19.37v  1768  axrep1  4564  kmlem14  8564  zfcndrep  9013  zfcndpow  9015  zfcndac  9018  dford4  30971  bj-axrep1  34374  bj-snsetex  34521 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747 This theorem depends on definitions:  df-bi 185  df-ex 1613
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