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Theorem 19.27h 1524
Description: Theorem 19.27 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
19.27h.1  |-  ( ps 
->  A. x ps )
Assertion
Ref Expression
19.27h  |-  ( A. x ( ph  /\  ps )  <->  ( A. x ph  /\  ps ) )

Proof of Theorem 19.27h
StepHypRef Expression
1 19.26 1442 . 2  |-  ( A. x ( ph  /\  ps )  <->  ( A. x ph  /\  A. x ps ) )
2 19.27h.1 . . . 4  |-  ( ps 
->  A. x ps )
3219.3h 1517 . . 3  |-  ( A. x ps  <->  ps )
43anbi2i 452 . 2  |-  ( ( A. x ph  /\  A. x ps )  <->  ( A. x ph  /\  ps )
)
51, 4bitri 183 1  |-  ( A. x ( ph  /\  ps )  <->  ( A. x ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    <-> wb 104   A.wal 1314
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-4 1472
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  aaanh  1550  19.27v  1855
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