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Theorem 19.28h 1542
Description: Theorem 19.28 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
19.28h.1  |-  ( ph  ->  A. x ph )
Assertion
Ref Expression
19.28h  |-  ( A. x ( ph  /\  ps )  <->  ( ph  /\  A. x ps ) )

Proof of Theorem 19.28h
StepHypRef Expression
1 19.26 1458 . 2  |-  ( A. x ( ph  /\  ps )  <->  ( A. x ph  /\  A. x ps ) )
2 19.28h.1 . . . 4  |-  ( ph  ->  A. x ph )
3219.3h 1533 . . 3  |-  ( A. x ph  <->  ph )
43anbi1i 454 . 2  |-  ( ( A. x ph  /\  A. x ps )  <->  ( ph  /\ 
A. x ps )
)
51, 4bitri 183 1  |-  ( A. x ( ph  /\  ps )  <->  ( ph  /\  A. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    <-> wb 104   A.wal 1330
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 1424  ax-gen 1426  ax-4 1488
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  nfan1  1544  aaanh  1566  exan  1672  19.28v  1873
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