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Theorem 19.27v 1771
Description: Version of 19.27 1928 with a dv condition, requiring fewer axioms. (Contributed by NM, 3-Jun-2004.)
Assertion
Ref Expression
19.27v  |-  ( A. x ( ph  /\  ps )  <->  ( A. x ph  /\  ps ) )
Distinct variable group:    ps, x
Allowed substitution hint:    ph( x)

Proof of Theorem 19.27v
StepHypRef Expression
1 19.26 1685 . 2  |-  ( A. x ( ph  /\  ps )  <->  ( A. x ph  /\  A. x ps ) )
2 19.3v 1760 . . 3  |-  ( A. x ps  <->  ps )
32anbi2i 692 . 2  |-  ( ( A. x ph  /\  A. x ps )  <->  ( A. x ph  /\  ps )
)
41, 3bitri 249 1  |-  ( A. x ( ph  /\  ps )  <->  ( A. x ph  /\  ps ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 367   A.wal 1396
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1618
This theorem is referenced by:  rexrsb  32413
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