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Theorem 19.27 1928
Description: Theorem 19.27 of [Margaris] p. 90. See 19.27v 1771 for a version requiring fewer axioms. (Contributed by NM, 21-Jun-1993.)
Hypothesis
Ref Expression
19.27.1  |-  F/ x ps
Assertion
Ref Expression
19.27  |-  ( A. x ( ph  /\  ps )  <->  ( A. x ph  /\  ps ) )

Proof of Theorem 19.27
StepHypRef Expression
1 19.26 1685 . 2  |-  ( A. x ( ph  /\  ps )  <->  ( A. x ph  /\  A. x ps ) )
2 19.27.1 . . . 4  |-  F/ x ps
3219.3 1893 . . 3  |-  ( A. x ps  <->  ps )
43anbi2i 692 . 2  |-  ( ( A. x ph  /\  A. x ps )  <->  ( A. x ph  /\  ps )
)
51, 4bitri 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   F/wnf 1621
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  ax-7 1795  ax-12 1859
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1618  df-nf 1622
This theorem is referenced by:  aaan  1980
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