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Theorem 19.38 1639
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 hbe1 1456 . . 3  |-  ( E. x ph  ->  A. x E. x ph )
2 hba1 1505 . . 3  |-  ( A. x ps  ->  A. x A. x ps )
31, 2hbim 1509 . 2  |-  ( ( E. x ph  ->  A. x ps )  ->  A. x ( E. x ph  ->  A. x ps )
)
4 19.8a 1554 . . 3  |-  ( ph  ->  E. x ph )
5 ax-4 1472 . . 3  |-  ( A. x ps  ->  ps )
64, 5imim12i 59 . 2  |-  ( ( E. x ph  ->  A. x ps )  -> 
( ph  ->  ps )
)
73, 6alrimih 1430 1  |-  ( ( E. x ph  ->  A. x ps )  ->  A. x ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1314   E.wex 1453
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-ie1 1454  ax-ie2 1455  ax-4 1472  ax-ial 1499  ax-i5r 1500
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  19.23t  1640  sbi2v  1848  mo3h  2030  rgenm  3435  ralm  3437
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