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Theorem 19.28v 1793
Description: Version of 19.28 1954 with a dv condition, requiring fewer axioms. (Contributed by NM, 25-Mar-2004.)
Assertion
Ref Expression
19.28v  |-  ( A. x ( ph  /\  ps )  <->  ( ph  /\  A. x ps ) )
Distinct variable group:    ph, x
Allowed substitution hint:    ps( x)

Proof of Theorem 19.28v
StepHypRef Expression
1 19.26 1703 . 2  |-  ( A. x ( ph  /\  ps )  <->  ( A. x ph  /\  A. x ps ) )
2 19.3v 1781 . . 3  |-  ( A. x ph  <->  ph )
32anbi1i 695 . 2  |-  ( ( A. x ph  /\  A. x ps )  <->  ( ph  /\ 
A. x ps )
)
41, 3bitri 251 1  |-  ( A. x ( ph  /\  ps )  <->  ( ph  /\  A. x ps ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 186    /\ wa 369   A.wal 1405
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773
This theorem depends on definitions:  df-bi 187  df-an 371  df-ex 1636
This theorem is referenced by:  reu6  3240  dfer2  7351  kmlem14  8577  kmlem15  8578  bnj1176  29401  bnj1186  29403  19.28vv  36152
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