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Theorem 19.38 1791
Description: Theorem 19.38 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
19.38  |-  ( ( E. x ph  ->  A. x ps )  ->  A. x ( ph  ->  ps ) )

Proof of Theorem 19.38
StepHypRef Expression
1 nfe1 1566 . . 3  |-  F/ x E. x ph
2 nfa1 1719 . . 3  |-  F/ x A. x ps
31, 2nfim 1735 . 2  |-  F/ x
( E. x ph  ->  A. x ps )
4 19.8a 1758 . . 3  |-  ( ph  ->  E. x ph )
5 ax-4 1692 . . 3  |-  ( A. x ps  ->  ps )
64, 5imim12i 55 . 2  |-  ( ( E. x ph  ->  A. x ps )  -> 
( ph  ->  ps )
)
73, 6alrimi 1706 1  |-  ( ( E. x ph  ->  A. x ps )  ->  A. x ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6   A.wal 1532   E.wex 1537
This theorem is referenced by:  pm10.53  26914
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540
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